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