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. 7531’
20. What is the spherical excess of a spherical polygon of four sides whose angles are 95, 112, 134, and 78. Ans. 59