CONGRATULATIONS TO THE FOLLOWING PASSERS:
1. GURRO, Ferlin Grace D.-------1.25
2. DAQUAIDO, Dimas Jr. N.-------1.75
3. ZOSA, Jose Christian M.------1.75
4. MURILLO, Christer Allan P.---1.75
5. ROSADO, Reymark C.-----------1.75
6. ADAMI, Mary Ann B.-----------2.0
7. SOCORIN, Rexford B.----------2.5
8. ADAMI, Rachiel H.------------2.5
9. MARCELLA, Romnick A.---------2.75
10. ALCAREZ, Ted Edward S.------2.75
11. LOPEZ, John Irish P.--------2.75
12. DAMAYO, Ted S.--------------2.75
13. CANTOS, Joebert S.----------2.75
14. SANDOVAL, Richard T.--------3.0
15. MONTEJO, Jestoni B.---------3.0
16. MACAWADIB, Jamael P.--------3.0
--------NOTHING FOLLOWS------------
The rest are either REMOVAL OR FAILED.
SUMMARY:
NUMBER OF PASSERS = 16
NUMBER OF REMOVALS = 16
NUMBER OF FAILURES = 2
COVERAGE: COMPLEX NUMBER TO EIGENVECTORS
SCHED: MONDAY, MARCH 18, 2013
TIME: 9:00 AM
ROOM: E 208
Tuesday, March 12, 2013
Sunday, March 10, 2013
Problem Set Batch 2
I lost connection last night. Here is the 2nd batch of problems. I'll be taking 9/20 problems. Enjoy solving....
11. Determine the volume of a right truncated triangular prism with the following definitions: Let the corners of the triangular base be defined by A, B, and C. The length of AB = 10 ft., BC = 9 ft., CA = 12 ft. The sides A, B, and C are perpendicular to the triangular base and have the height of 8.68 ft., 7.1 ft. and 5.5 ft. respectively. Ans. 311 ft3
12. A circular cylinder is circumscribed about a right prism having a square base one meter on an edge. The volume of the cylinder is 6.283 cu.m. Find its altitude in meters. Ans. 4m
13. The bases of a right prism is a hexagon with one of each side is equal to 6 cm. The bases are 12 cm apart. What is the volume of the right prism? Ans. 1122.4 cm3
14. A circular cylinder with a volume of 6.54 cu. m. is circumscribed about a right prism whose base is an equilateral triangle of a side 1.25 m. What is the altitude of the cylinder in meters? Ans. 4
15. The central angle of a spherical wedge is 1 radian. Find its volume if its radius is 1 unit. Ans. 2/3
16. The volume of water in a spherical tank having a diameter of 4 m is 5.236 m3. Determine the depth of the water in the tank. Ans. 1m
17. Water is poured to a depth of 12 cm into a hemispherical bowl of radius 20 cm. Find the volume of the water. Ans. 2304π cm3
18. A hemisphere whose radius is 12 inches is surmounted by a right circular cone with the same radius and an altitude of 15 inches. Find the total volume. Ans. 5881. 06 in3
19. The lateral area of a right circular cone is 4 times the area of the base. Find the angle at which an element of the cone is inclined to the base. Ans. 7531’
20. What is the spherical excess of a spherical polygon of four sides whose angles are 95, 112, 134, and 78. Ans. 59
11. Determine the volume of a right truncated triangular prism with the following definitions: Let the corners of the triangular base be defined by A, B, and C. The length of AB = 10 ft., BC = 9 ft., CA = 12 ft. The sides A, B, and C are perpendicular to the triangular base and have the height of 8.68 ft., 7.1 ft. and 5.5 ft. respectively. Ans. 311 ft3
12. A circular cylinder is circumscribed about a right prism having a square base one meter on an edge. The volume of the cylinder is 6.283 cu.m. Find its altitude in meters. Ans. 4m
13. The bases of a right prism is a hexagon with one of each side is equal to 6 cm. The bases are 12 cm apart. What is the volume of the right prism? Ans. 1122.4 cm3
14. A circular cylinder with a volume of 6.54 cu. m. is circumscribed about a right prism whose base is an equilateral triangle of a side 1.25 m. What is the altitude of the cylinder in meters? Ans. 4
15. The central angle of a spherical wedge is 1 radian. Find its volume if its radius is 1 unit. Ans. 2/3
16. The volume of water in a spherical tank having a diameter of 4 m is 5.236 m3. Determine the depth of the water in the tank. Ans. 1m
17. Water is poured to a depth of 12 cm into a hemispherical bowl of radius 20 cm. Find the volume of the water. Ans. 2304π cm3
18. A hemisphere whose radius is 12 inches is surmounted by a right circular cone with the same radius and an altitude of 15 inches. Find the total volume. Ans. 5881. 06 in3
19. The lateral area of a right circular cone is 4 times the area of the base. Find the angle at which an element of the cone is inclined to the base. Ans. 7531’
20. What is the spherical excess of a spherical polygon of four sides whose angles are 95, 112, 134, and 78. Ans. 59
Saturday, March 9, 2013
Solid Mensuration Problem Set
This is just the first batch of problems. Enjoy Solving.
1. Each side of the cube is increased by 1%. By what percent is the volume of the cube increased? Ans. 3.03%
2.Given a sphere of diameter d, what is the percentage increase in its diameter when the surface area increases by 21% Ans. 10%
3. How many times does the volume of the sphere increase if the radius is doubled? Ans. 8 times
4. A circular cone having an altitude of 9 m is divided into two segments having the same vertex. If the smaller altitude is 6 m, find the ratio of the volume of the small cone to the big cone. Ans. 0.296
5. Find the volume of the cone to be constructed from a sector having a diameter of 72 cm and a central angle of 210. Ans. 13503.4 cu. cm.
6. What is the height of a circular cone having a slant height of √(10x ) and a base diameter of 2x? Ans. 3x
7. The ratio of the volume to the lateral area of a right circular cone is 2:1. If the altitude is 15 cm, what is the ratio of the slant height to the radius? Ans. 5:2
8. A regular triangular pyramid has an altitude of 9m and a volume of 187.06 cu. m. What is the base edge in meters? Ans. 12m
9. The volume of the frustum of a regular triangular pyramid is 135 cu.m. The lower base is an equilateral triangle with an edge of 9 cm. The upper base is 8 m above the lower base. What is the upper base edge in meters? Ans. 3m
10. What is the frustum of a cone whose upper base is 15 cm in diameter and lower base 10 cm. in diameter with an altitude of 25 cm? Ans. 3108.87 cm3
1. Each side of the cube is increased by 1%. By what percent is the volume of the cube increased? Ans. 3.03%
2.Given a sphere of diameter d, what is the percentage increase in its diameter when the surface area increases by 21% Ans. 10%
3. How many times does the volume of the sphere increase if the radius is doubled? Ans. 8 times
4. A circular cone having an altitude of 9 m is divided into two segments having the same vertex. If the smaller altitude is 6 m, find the ratio of the volume of the small cone to the big cone. Ans. 0.296
5. Find the volume of the cone to be constructed from a sector having a diameter of 72 cm and a central angle of 210. Ans. 13503.4 cu. cm.
6. What is the height of a circular cone having a slant height of √(10x ) and a base diameter of 2x? Ans. 3x
7. The ratio of the volume to the lateral area of a right circular cone is 2:1. If the altitude is 15 cm, what is the ratio of the slant height to the radius? Ans. 5:2
8. A regular triangular pyramid has an altitude of 9m and a volume of 187.06 cu. m. What is the base edge in meters? Ans. 12m
9. The volume of the frustum of a regular triangular pyramid is 135 cu.m. The lower base is an equilateral triangle with an edge of 9 cm. The upper base is 8 m above the lower base. What is the upper base edge in meters? Ans. 3m
10. What is the frustum of a cone whose upper base is 15 cm in diameter and lower base 10 cm. in diameter with an altitude of 25 cm? Ans. 3108.87 cm3
Sunday, February 3, 2013
CIRCUITS II PROBLEM SETS (SERIES CIRCUIT)
1. An impedance coil is connected in series with a fixed resistor, and a 120 – V 25 cycle source is then impressed across the combination. If the voltage drops across the coil and resistor are 70 and 80 volts, respectively, when the current is 1.4 A, find the resistance of the coil. Ans. 13.84 Ω
2. A circuit consisting of a non –inductive resistance in series with a condenser is connected in series with a non – inductive resistance of 2 ohm across 220 volts, 25 – Hz mains. What is the capacitance when the entire circuit takes 300 W at a power factor of 0.2? Ans. 201 micro -Farad
3. A non – inductive resistance is in series with a condenser takes 7A and absorbs 300 W when connected across a 110 – V, 25 Hz mains. What non – inductive resistance must be connected in series with the circuit in order that it may take the same current from a 110 – V, 60 Hz supply? Ans. 8.38Ω
4. Find the value of impedance which absorbs a complex power of 5000∠45deg volt – amperes when the rms current through it is 12.5 A. Ans. 22.62 + j22.62 Ω
5. The resistance R and L of a coil are to be determined experimentally. The available equipment is a voltmeter and an 8 – ohm resistor. The 8 – ohm resistor is connected in series with the coil and the combination across a 120 V, 60 Hz source. If the voltmeter reads 32 V across the resistor, and 104 V across the coil, Find L. Ans. 63. 66mH
6. What is the inductance of the coil if it draws 0.55 A from a 110 – V, 60 Hz power line and 0.2 A from a 20 V battery? Ans. 0.459 H
7. A 5 micro-F capacitor is connected in series with a variable inductor to a 20 – V, 796 cycle source. For what value of inductance will the current be 2A leading? Ans. 6mH
8. An impedance coil is connected in series with a condenser across 220 – volt, 60 Hz source. The circuit absorbs 800 W at a power factor of 0.4 lagging and is so adjusted that the voltage across the condenser is 350 V. What is the voltage across the impedance coil? Ans. 558. 6 V
9. A coil draws 10 A when connected across a 100 V source. When a 10 – ohm resistor is connected in series with the coil, the current is reduced to 6 A. Determine the resistance of the coil. Ans. 3.89Ω
10. Find the current that will flow in a series circuit containing a 5 kΩ resistor, a 470 pF capacitor, a 150mH inductor, and a 0.001 micro-Farad capacitor if the exciting voltage is 65 V at 25Khz. Ans. 10.5 mA
1. An impedance coil is connected in series with a fixed resistor, and a 120 – V 25 cycle source is then impressed across the combination. If the voltage drops across the coil and resistor are 70 and 80 volts, respectively, when the current is 1.4 A, find the resistance of the coil. Ans. 13.84 Ω
2. A circuit consisting of a non –inductive resistance in series with a condenser is connected in series with a non – inductive resistance of 2 ohm across 220 volts, 25 – Hz mains. What is the capacitance when the entire circuit takes 300 W at a power factor of 0.2? Ans. 201 micro -Farad
3. A non – inductive resistance is in series with a condenser takes 7A and absorbs 300 W when connected across a 110 – V, 25 Hz mains. What non – inductive resistance must be connected in series with the circuit in order that it may take the same current from a 110 – V, 60 Hz supply? Ans. 8.38Ω
4. Find the value of impedance which absorbs a complex power of 5000∠45deg volt – amperes when the rms current through it is 12.5 A. Ans. 22.62 + j22.62 Ω
5. The resistance R and L of a coil are to be determined experimentally. The available equipment is a voltmeter and an 8 – ohm resistor. The 8 – ohm resistor is connected in series with the coil and the combination across a 120 V, 60 Hz source. If the voltmeter reads 32 V across the resistor, and 104 V across the coil, Find L. Ans. 63. 66mH
6. What is the inductance of the coil if it draws 0.55 A from a 110 – V, 60 Hz power line and 0.2 A from a 20 V battery? Ans. 0.459 H
7. A 5 micro-F capacitor is connected in series with a variable inductor to a 20 – V, 796 cycle source. For what value of inductance will the current be 2A leading? Ans. 6mH
8. An impedance coil is connected in series with a condenser across 220 – volt, 60 Hz source. The circuit absorbs 800 W at a power factor of 0.4 lagging and is so adjusted that the voltage across the condenser is 350 V. What is the voltage across the impedance coil? Ans. 558. 6 V
9. A coil draws 10 A when connected across a 100 V source. When a 10 – ohm resistor is connected in series with the coil, the current is reduced to 6 A. Determine the resistance of the coil. Ans. 3.89Ω
10. Find the current that will flow in a series circuit containing a 5 kΩ resistor, a 470 pF capacitor, a 150mH inductor, and a 0.001 micro-Farad capacitor if the exciting voltage is 65 V at 25Khz. Ans. 10.5 mA
Friday, February 1, 2013
RATIO PROPORTION AND VARIATION PROBLEM SETS
1. Mr. Tan had some local stamps and foreign stamps. The number of local stamps was 2/3 that of foreign stamps. Some local stamps were given away and the number of local stamps became 2/5 that of the foreign stamps. If there were 200 local stamps at first, how many of them were given away? Ans. 80
2. The number of boys, girls and adults at a marathon was in the ratio 5:8:2. When some girls left the marathon, the new ratio became 10:9:4. If there were 150 participants altogether, how many girls left the marathon? Ans. 35
3. Jane and Wendy had stickers in the ratio 4:5. After Jane gave 60 stickers away, the new ratio became 3:10. How many stickers did Wendy have? Ans. 120
4. The cost of labor varies jointly as the number of workers and the number of days they work. If 8 men working 9 days each are paid P576, in how many days it take 6 men to earn P624? Ans. 13
5. In a certain factory, the ratio of the number of male to female workers is 2:3. If one hundred new female workers are hired, the number of female workers will increase to 65% of the total number of workers. Find the original number of workers in the factory. Ans. 700
6. The amount of electric current required to melt a fuse varies as the three halves power of the diameter. If the current required to melt a wire of diameter 0.02 in is 15 amperes, what current will be required to melt a wire of the same material having a diameter of 0.08 inch? Ans. 120
7. If the ratio of the measures of the interior angles of a quadrilaterals is 2:3:4:6, what is the measure of the smallest angle of the quadrilateral? Ans. 48
8. The horsepower which a shaft can transmit varies as the cube of the diameter and the angular speed. If a 75 – mm diameter shaft transmit 270 hp when turning 1000 rpm, find the horsepower which can be transmitted by a 125 mm shaft rotating 1500 rpm. Ans. 1875
9. Two numbers have the ratio 3:4 and if 7 is subtracted from each, the remainder is 2:3. Find the smaller number between the two. Ans. 21
10. A flagpole cast a shadow of 7.5 ft. Find the height of the flagpole if a meter stick cast a shadow of 50 cm. Ans. 15 ft.
11. One photograph is 2 cm by 3 cm. If the width and length of another photograph are each double the first, what is the ratio of their areas? Ans. 1:4
12. Aling Felisa, a dressmaker, can sew a dress in 2/3 of a day. About how many days will it take her to finish 18 dresses? Ans. 12
13. The areas of two similar triangles are in the ratio of 4:1. If the length of the side of the smaller triangle is 5 units, what is the length of the corresponding side of the larger triangle? Ans. 10
14. The ratio of the lengths of the legs of a right triangle is 3:4. If the hypotenuse is 20 cm, find the length of the longer leg? Ans. 16 cm
15. If a kilogram of fertilizer can fertilize 10 square meters of garden area, how many square centimeters can ¼ kilogram fertilize? Ans. 25, 000 sq cm
16. The ratio of men to women in a certain party was 5:3. Twenty – four men got drunk and decided to leave the party. When twenty – four more women joined the party, the ratio between men to women was interchanged. How many men were left in the party? Ans. 36
17. The ages of Tom, Jerry, and Troy are in the ratio 2:3:6 now. In 5 years, their ages will be in the ratio of 3:4:7. How old is Troy? Ans. 30
18. The current in a wire varies directly as the electromotive force and inversely as the resistance. If the current = 12 amperes when voltage = 120 volts and resistance = 6 ohms, find the current when voltage = 220 volts and resistance = 10 ohms. Ans. 13.2 amperes
19. If the areas of two circles are 48 and 75, find the ratio of their circumferences. Ans. 4:5
20. If H is proportional to x and inversely proportional to∛y, and if H = 4 when x = 3 and y = 8, find H if y = 4 and x = 5. Ans. 20/3 ∛2
1. Mr. Tan had some local stamps and foreign stamps. The number of local stamps was 2/3 that of foreign stamps. Some local stamps were given away and the number of local stamps became 2/5 that of the foreign stamps. If there were 200 local stamps at first, how many of them were given away? Ans. 80
2. The number of boys, girls and adults at a marathon was in the ratio 5:8:2. When some girls left the marathon, the new ratio became 10:9:4. If there were 150 participants altogether, how many girls left the marathon? Ans. 35
3. Jane and Wendy had stickers in the ratio 4:5. After Jane gave 60 stickers away, the new ratio became 3:10. How many stickers did Wendy have? Ans. 120
4. The cost of labor varies jointly as the number of workers and the number of days they work. If 8 men working 9 days each are paid P576, in how many days it take 6 men to earn P624? Ans. 13
5. In a certain factory, the ratio of the number of male to female workers is 2:3. If one hundred new female workers are hired, the number of female workers will increase to 65% of the total number of workers. Find the original number of workers in the factory. Ans. 700
6. The amount of electric current required to melt a fuse varies as the three halves power of the diameter. If the current required to melt a wire of diameter 0.02 in is 15 amperes, what current will be required to melt a wire of the same material having a diameter of 0.08 inch? Ans. 120
7. If the ratio of the measures of the interior angles of a quadrilaterals is 2:3:4:6, what is the measure of the smallest angle of the quadrilateral? Ans. 48
8. The horsepower which a shaft can transmit varies as the cube of the diameter and the angular speed. If a 75 – mm diameter shaft transmit 270 hp when turning 1000 rpm, find the horsepower which can be transmitted by a 125 mm shaft rotating 1500 rpm. Ans. 1875
9. Two numbers have the ratio 3:4 and if 7 is subtracted from each, the remainder is 2:3. Find the smaller number between the two. Ans. 21
10. A flagpole cast a shadow of 7.5 ft. Find the height of the flagpole if a meter stick cast a shadow of 50 cm. Ans. 15 ft.
11. One photograph is 2 cm by 3 cm. If the width and length of another photograph are each double the first, what is the ratio of their areas? Ans. 1:4
12. Aling Felisa, a dressmaker, can sew a dress in 2/3 of a day. About how many days will it take her to finish 18 dresses? Ans. 12
13. The areas of two similar triangles are in the ratio of 4:1. If the length of the side of the smaller triangle is 5 units, what is the length of the corresponding side of the larger triangle? Ans. 10
14. The ratio of the lengths of the legs of a right triangle is 3:4. If the hypotenuse is 20 cm, find the length of the longer leg? Ans. 16 cm
15. If a kilogram of fertilizer can fertilize 10 square meters of garden area, how many square centimeters can ¼ kilogram fertilize? Ans. 25, 000 sq cm
16. The ratio of men to women in a certain party was 5:3. Twenty – four men got drunk and decided to leave the party. When twenty – four more women joined the party, the ratio between men to women was interchanged. How many men were left in the party? Ans. 36
17. The ages of Tom, Jerry, and Troy are in the ratio 2:3:6 now. In 5 years, their ages will be in the ratio of 3:4:7. How old is Troy? Ans. 30
18. The current in a wire varies directly as the electromotive force and inversely as the resistance. If the current = 12 amperes when voltage = 120 volts and resistance = 6 ohms, find the current when voltage = 220 volts and resistance = 10 ohms. Ans. 13.2 amperes
19. If the areas of two circles are 48 and 75, find the ratio of their circumferences. Ans. 4:5
20. If H is proportional to x and inversely proportional to∛y, and if H = 4 when x = 3 and y = 8, find H if y = 4 and x = 5. Ans. 20/3 ∛2
Saturday, January 12, 2013
Problem Set for Plane and Solid Geometry Midterm Coverage:
1. If the lateral area of the right circular cylinder is 88 and its volume is 220, find its radius. Ans. 5
2. A prism has an equilateral triangle with 20 cm on a side for its base, and an altitude of 30 cm. Determine its lateral area. Ans. 1800 sq. cm.
3. How many sides have a regular polygon, if each interior angle is 165 deg? Ans. 24
4. The area of a hexagon inscribed in a circle is 374.11 sq cm. Determine the area of the circle. Ans. 452.39 sq. cm.
5. A polygon has 170 diagonals. How many sides does it have? Ans. 20
6. The circumference of the base of a right circular cylinder is 48 cm and its altitude is 15 cm. Determine its total surface area. Ans. 1086.69 sq. cm.
7. A rectangle is inscribed in a circle whose radius is 5 inches. The base of the rectangle is 8 inches. Find the area of the rectangle. Ans. 48 sq. in.
8. Find the length of the side of a pentagon if the line perpendicular to its side is 12 units from the center. Ans. 17.44 units
9. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the dodecagon. Ans. 149.08
10. Find the area of the rhombus if one diagonal has length 30 and a side has length 17. Ans. 240
11. The area of the rhombus is 168 sq. m. If one of the diagonal is 12 m, find the length of the sides of a rhombus. Ans. 15.23 cm
12. The sum of the interior angles of a polygon is 540 deg. Find the number of sides. Ans. 5
13. How many diagonals are there in a polygon if it has 16 sides? Ans. 104
14. In a square, find the length of the apothem if the radius of the circumscribing circle is 16. Ans. 11.31
15. The bases of a right prism are regular hexagons with each side equal to 6 cm. The bases are 10 cm apart. What is the volume of the prism? Ans. 935.31 sq. cm.
16. What is the volume of a right circular cylinder inscribed in a cube of edge 10 cm? Ans. 785.4 sq. cm.
17. The volume of the prism with an altitude of 15 m and having an equilateral triangle as its base is equal to 234 sq. m. Determine the length of the side of the triangular base. Ans. 6 m
18. The area of a hexagon is 54√3. Determine the length of each side. Ans. 6
19. The wall at one end of an attic takes the shape of a trapezoid because of a slanted ceiling. The wall is 8 ft high at one end, 10 ft wide and only 3 ft high on the other end. Determine the area of the wall in sq. ft. Ans. 55
20. The bases of a right prism are a hexagon with one side 6 cm long. If the volume of the prism is 450 cu cm, how apart are the bases? Ans. 4.81 cm
21. Find the length of the diagonal of a cube whose volume is 729 cu. cm. Ans. 15.59 cm
22. If the sides of a parallelogram and an included angle are 6, 10 and 100, respectively, find the length of the shorter diagonal. Ans. 10.73
23. Three circles C1, C2, and C3 are externally tangent to each other. Center to center distances are 10 cm between C1 and C2, 8 cm between C2 and C3 and 6 cm between C3 and C1. Determine the total areas of the circles. Ans. 175.93 sq. cm.
24. Find the area of a regular pentagon whose side is 25 cm and apothem is 17.2 cm. Ans. 1075 sq. cm.
25. For a regular polygon of heptagon sides, find the number of degrees contained in each central angle. Ans. 51.43 deg
26. A regular octagon is inscribed in a circle. What is the radius of the circle if the length of each side of the octagon is 12.6 inches? Ans. 16. 46 in
27. A circle with radius 6 cm has half its area removed by cutting off a border of uniform width. Find the width of the border. Ans. 1.76 cm
28. Find the number of degrees in the measure of each exterior angle of a regular polygon which has 12 sides. Ans. 150
29. The altitude of a parallelepiped is 20 cm and the base is a rhombus with diagonals 14 cm and 48 cm. Find the volume of the parallelepiped. Ans. 6720 cu. cm.
30. The diagonal of the face of the cube is 3√2. Find the diagonal of the cube. Ans. 3√3.
31. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the dodecagon. Ans. 149.08
32. The volume of the rectangular solid is 480 cu. cm. If the base is 8 cm by 10 cm, find the total area of the solid. Ans. 376 sq. cm.
33. A cylindrical tank with horizontal axis has a radius of 1m and 6 m long. If it is filled with gasoline to a depth of 1.3m, determine the volume of the gasoline in the tank. Ans. 12.97 cu. m.
34. An open box with a square base is to be constructed from a square piece of tin by cutting out a 3 – inch square from each corner and folding up the sides. If the box is to hold 48 cubic inches, what must be the length of the side of tin? Ans.10 in
35. The volume of a rectangular parallelepiped is 1944 cu. cm. The edges are in the ratio 3:4:6. Determine the length of the shortest edge? Ans. 9
36. The area of a circle circumscribing a hexagon is 452. 39 sq. m. Find the area of the hexagon. Ans. 374. 12
37. Find the area of the inscribed circle of a regular hexagon whose side has a length of 8 cm. Ans. 201. 06 sq. cm.
38. A regular hexagonal prism is inscribed in a right circular cylinder whose lateral edge is 10 cm and the radius of base is 3cm. Compute the volume of the prism. Ans. 234 cu. cm.
39. The length of the diagonal of the rhombus are 30 cm and 40 cm respectively. Find the perimeter of the rhombus. Ans. 100 cm.
40. The base of a right prism is an equilateral triangle 3 cm on a side. If its altitude is 8 cm, find its volume. Ans. 31.18 cu. cm.
41. A piece of wire is shaped to enclose a square whose area is 169 sq. in. It is then reshaped to form a rectangle whose length is 15 in. Determine the area of the rectangle. Ans. 165 sq. in.
42. The base area of a circular cylinder is 12 sq. cm. and an element of the cylinder is 10 cm. Find the volume of the cylinder if the element is inclined to the base an angle of 60 deg. 103.92 cu. cm.
43. The corner of a 2 - meter square is cut off to form a regular octagon. Determine the length of the resulting side of the octagon. Ans. 0.828 m
44. The area of the rectangular lot is increased by 25 sq. m. if it longer by 10 m and narrower by 2.5 m. Also when it is shorter by 10 m and wider by 5 m, its area is reduced by 50 sq. m. Solve the original area. Ans. 200 sq. m.
45. A right hexagonal prism is inscribed in a right circular cylinder whose height is 20 cm. The difference between the circumference of the circle and the perimeter of the hexagon 4 cm. Determine the volume of the prism. Ans. 10367.18 cu. cm.
46. An irrigation canal is 200 m long and 2 m deep. It is 2 m wide at the top and 1 m at the bottom. Find the volume excavated to make the canal. Ans. 600 cu. m.
47. A room is 12 ft wide, 15 ft long and 8 ft high. If an air conditioner changes the air once every five minutes, how many cubic feet of air does it change per hour? Ans. 17280
48. The volume of a rectangular parallelepiped is 15, 000 cu. m. and its total surface area is 3,700 sq. cm. If its altitude is 20 cm, find the dimension of the shorter side of the base. Ans. 25 cm
49. The circumference of the base of a closed right circular cylinder is 48 cm and its altitude is 15 cm. Determine its total surface area. 1086. 69 sq. cm.
50. A circular cylinder with a volume of 6.54 cubic meters is circumscribed about a right prism whose base is an equilateral triangle of side 1.25 m. What is the altitude of the cylinder? Ans. 4m
1. If the lateral area of the right circular cylinder is 88 and its volume is 220, find its radius. Ans. 5
2. A prism has an equilateral triangle with 20 cm on a side for its base, and an altitude of 30 cm. Determine its lateral area. Ans. 1800 sq. cm.
3. How many sides have a regular polygon, if each interior angle is 165 deg? Ans. 24
4. The area of a hexagon inscribed in a circle is 374.11 sq cm. Determine the area of the circle. Ans. 452.39 sq. cm.
5. A polygon has 170 diagonals. How many sides does it have? Ans. 20
6. The circumference of the base of a right circular cylinder is 48 cm and its altitude is 15 cm. Determine its total surface area. Ans. 1086.69 sq. cm.
7. A rectangle is inscribed in a circle whose radius is 5 inches. The base of the rectangle is 8 inches. Find the area of the rectangle. Ans. 48 sq. in.
8. Find the length of the side of a pentagon if the line perpendicular to its side is 12 units from the center. Ans. 17.44 units
9. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the dodecagon. Ans. 149.08
10. Find the area of the rhombus if one diagonal has length 30 and a side has length 17. Ans. 240
11. The area of the rhombus is 168 sq. m. If one of the diagonal is 12 m, find the length of the sides of a rhombus. Ans. 15.23 cm
12. The sum of the interior angles of a polygon is 540 deg. Find the number of sides. Ans. 5
13. How many diagonals are there in a polygon if it has 16 sides? Ans. 104
14. In a square, find the length of the apothem if the radius of the circumscribing circle is 16. Ans. 11.31
15. The bases of a right prism are regular hexagons with each side equal to 6 cm. The bases are 10 cm apart. What is the volume of the prism? Ans. 935.31 sq. cm.
16. What is the volume of a right circular cylinder inscribed in a cube of edge 10 cm? Ans. 785.4 sq. cm.
17. The volume of the prism with an altitude of 15 m and having an equilateral triangle as its base is equal to 234 sq. m. Determine the length of the side of the triangular base. Ans. 6 m
18. The area of a hexagon is 54√3. Determine the length of each side. Ans. 6
19. The wall at one end of an attic takes the shape of a trapezoid because of a slanted ceiling. The wall is 8 ft high at one end, 10 ft wide and only 3 ft high on the other end. Determine the area of the wall in sq. ft. Ans. 55
20. The bases of a right prism are a hexagon with one side 6 cm long. If the volume of the prism is 450 cu cm, how apart are the bases? Ans. 4.81 cm
21. Find the length of the diagonal of a cube whose volume is 729 cu. cm. Ans. 15.59 cm
22. If the sides of a parallelogram and an included angle are 6, 10 and 100, respectively, find the length of the shorter diagonal. Ans. 10.73
23. Three circles C1, C2, and C3 are externally tangent to each other. Center to center distances are 10 cm between C1 and C2, 8 cm between C2 and C3 and 6 cm between C3 and C1. Determine the total areas of the circles. Ans. 175.93 sq. cm.
24. Find the area of a regular pentagon whose side is 25 cm and apothem is 17.2 cm. Ans. 1075 sq. cm.
25. For a regular polygon of heptagon sides, find the number of degrees contained in each central angle. Ans. 51.43 deg
26. A regular octagon is inscribed in a circle. What is the radius of the circle if the length of each side of the octagon is 12.6 inches? Ans. 16. 46 in
27. A circle with radius 6 cm has half its area removed by cutting off a border of uniform width. Find the width of the border. Ans. 1.76 cm
28. Find the number of degrees in the measure of each exterior angle of a regular polygon which has 12 sides. Ans. 150
29. The altitude of a parallelepiped is 20 cm and the base is a rhombus with diagonals 14 cm and 48 cm. Find the volume of the parallelepiped. Ans. 6720 cu. cm.
30. The diagonal of the face of the cube is 3√2. Find the diagonal of the cube. Ans. 3√3.
31. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the dodecagon. Ans. 149.08
32. The volume of the rectangular solid is 480 cu. cm. If the base is 8 cm by 10 cm, find the total area of the solid. Ans. 376 sq. cm.
33. A cylindrical tank with horizontal axis has a radius of 1m and 6 m long. If it is filled with gasoline to a depth of 1.3m, determine the volume of the gasoline in the tank. Ans. 12.97 cu. m.
34. An open box with a square base is to be constructed from a square piece of tin by cutting out a 3 – inch square from each corner and folding up the sides. If the box is to hold 48 cubic inches, what must be the length of the side of tin? Ans.10 in
35. The volume of a rectangular parallelepiped is 1944 cu. cm. The edges are in the ratio 3:4:6. Determine the length of the shortest edge? Ans. 9
36. The area of a circle circumscribing a hexagon is 452. 39 sq. m. Find the area of the hexagon. Ans. 374. 12
37. Find the area of the inscribed circle of a regular hexagon whose side has a length of 8 cm. Ans. 201. 06 sq. cm.
38. A regular hexagonal prism is inscribed in a right circular cylinder whose lateral edge is 10 cm and the radius of base is 3cm. Compute the volume of the prism. Ans. 234 cu. cm.
39. The length of the diagonal of the rhombus are 30 cm and 40 cm respectively. Find the perimeter of the rhombus. Ans. 100 cm.
40. The base of a right prism is an equilateral triangle 3 cm on a side. If its altitude is 8 cm, find its volume. Ans. 31.18 cu. cm.
41. A piece of wire is shaped to enclose a square whose area is 169 sq. in. It is then reshaped to form a rectangle whose length is 15 in. Determine the area of the rectangle. Ans. 165 sq. in.
42. The base area of a circular cylinder is 12 sq. cm. and an element of the cylinder is 10 cm. Find the volume of the cylinder if the element is inclined to the base an angle of 60 deg. 103.92 cu. cm.
43. The corner of a 2 - meter square is cut off to form a regular octagon. Determine the length of the resulting side of the octagon. Ans. 0.828 m
44. The area of the rectangular lot is increased by 25 sq. m. if it longer by 10 m and narrower by 2.5 m. Also when it is shorter by 10 m and wider by 5 m, its area is reduced by 50 sq. m. Solve the original area. Ans. 200 sq. m.
45. A right hexagonal prism is inscribed in a right circular cylinder whose height is 20 cm. The difference between the circumference of the circle and the perimeter of the hexagon 4 cm. Determine the volume of the prism. Ans. 10367.18 cu. cm.
46. An irrigation canal is 200 m long and 2 m deep. It is 2 m wide at the top and 1 m at the bottom. Find the volume excavated to make the canal. Ans. 600 cu. m.
47. A room is 12 ft wide, 15 ft long and 8 ft high. If an air conditioner changes the air once every five minutes, how many cubic feet of air does it change per hour? Ans. 17280
48. The volume of a rectangular parallelepiped is 15, 000 cu. m. and its total surface area is 3,700 sq. cm. If its altitude is 20 cm, find the dimension of the shorter side of the base. Ans. 25 cm
49. The circumference of the base of a closed right circular cylinder is 48 cm and its altitude is 15 cm. Determine its total surface area. 1086. 69 sq. cm.
50. A circular cylinder with a volume of 6.54 cubic meters is circumscribed about a right prism whose base is an equilateral triangle of side 1.25 m. What is the altitude of the cylinder? Ans. 4m
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