# Volume and surface area Questions and answers

Topics

31). What is the difference in radii of the ends of the frustum?
 A). $$\Large \frac{\sqrt{Q - \sqrt{P}}}{\sqrt{ \pi }}$$ B). $$\Large \frac{\sqrt{Q - \sqrt{P}}}{ \pi }$$ C). $$\Large \sqrt{Q} - \sqrt{P}$$ D). None of the above.
32). What is the volume of the frustum?
 A). $$\Large 3H \left(P+Q+\sqrt{PQ}\right)$$ B). $$\Large H \left(P+Q+\sqrt{PQ}\right)$$ C). $$\Large H \frac{ \left(P+Q+\sqrt{PQ}\right) }{3}$$ D). $$\Large H \frac{ \left(P+Q-\sqrt{PQ}\right) }{3}$$
33). The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by
 A). 30% B). 31% C). 32.25% D). 34.75%
34). What will be the surface area of the sphere having 4 cm radius?
 A). 64 $$\Large \pi cm^{2}$$ B). 69 $$\Large \pi cm^{2}$$ C). 32 $$\Large \pi cm^{3}$$ D). 35 $$\Large \pi cm^{3}$$
35). What is the diameter of the largest circle lying on the surface of a Sphere of surface area 616 sq cm?
 A). 14 cm B). 10.5 cm C). 7 cm D). 3.5 cm

36). A sphere and a hemisphere have the same surface area. The ratio of their volumes is
 A). $$\Large \frac{\sqrt{3}}{4} : 1$$ B). $$\Large 3\frac{\sqrt{3}}{4} : 1$$ C). $$\Large \frac{\sqrt{3}}{8} : 1$$ D). $$\Large \frac{3\sqrt{3}}{8} : 1$$
37). A hemispherical bowl has 3.5 cm radius. It is to he painted inside as well as outside. Find the cost of painting it at the rate of Rs.5 per 10 sq cm.
 A). Rs.50 B). Rs.81 C). Rs.56 D). Rs.77
38). If the surface area of a sphere is 616 sq cm, What is its volume?
 A). $$\Large \frac{4312}{3} cm^{3}$$ B). $$\Large \frac{4102}{3} cm^{3}$$ C). $$\Large 1257 cm^{3}$$ D). $$\Large 1023 cm^{3}$$
39). If the ratio of the diameters of two spheres is 3 : 5, then What is the ratio of their surface areas?
 A). 9 : 25 B). 9 : 10 C). 3 : 5 D). 27 : 125
40). A hemisphere has 28 cm diameter. Find its curved surface area.
 A). 1232 sq cm B). 1236 sq cm C). 1238 sq cm D). 1233 sq cm
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