What is the formula for the volume of a sphere with radius r?
a)
43πr3b)
πr2c)
4πr3d)
πr3Answer: a)
43πr3What is the total surface area of a cube with edge ?
a) 6 a
b)
6a2c)
a3d)
2a2Answer: b)
6a2Which of the following is the curved surface area of a cylinder with radius and height ?
a)
πr2hb)
2πrhc)
2πr2hd)
πr2Answer: b)
2πrhWhat is the formula for the volume of a cone with radius and height ?
a)
πr2hb)
13πr2hc)
43πr3d)
2πrhAnswer: b)
13πr2hThe total surface area of a sphere is given by:
a)
b)
3πr2c)
4πr2d)
πr2Answer: c)
4πr2A solid cylinder has a height of 10 cm and base radius 3 cm. What is its volume? Use
π=3.14
a)
282.6 cm3b)
188.4 cm3c)
100 cm3d)
300 cm3Answer: a)
282.6 cm3The radius of a sphere is doubled. By what factor does the volume increase?
a) 2
b) 4
c) 6
d) 8
Answer: d) 8
Find the curved surface area of a cone with radius 7 cm and slant height 10 cm. Use
π=227
a)
220 cm2b)
154 cm2c)
140 cm2d)
200 cm2Answer: a)
220 cm2The height of a cylinder is twice the radius of its base. What is the ratio of its volume to the total surface area?
a) 1:1
b) 2:1
c) 3:1
d) 4:1
Answer: b) 2:1
A cone and a cylinder have the same radius and height. What is the ratio of their volumes?
a) 1:1
b) 1:2
c) 1:3
d) 2:3
Answer: c) 1:3
A toy is in the form of a hemisphere surmounted by a cone. If the height of the cone is 6 cm and the diameter of the hemisphere is 4 cm, find the volume of the toy. Use
π=3.14
a)
100.48 cm3b)
102.67 cm3c)
120.48 cm3120.48 \, \text{cm}^3d)
130 cm3130 \, \text{cm}^3Answer: b)
102.67 cm3A cylindrical vessel is filled with water and has a height of 10 cm and radius 7 cm. If a solid sphere with radius 3 cm is immersed, what will be the new height of the water level? Use
π=227
a) 10.45cm
b) 10.36cm
c) 10.50cm
d) 10.30cm
Answer: b) 10.36cm
A hollow cylindrical pipe has an external radius of 5 cm and an internal radius of 3 cm. If the height of the pipe is 10 cm, find the volume of the material used. Use
π=3.14
a)
376.8 cm3b)
400 cm3c)
452.16 cm3d)
500 cm3Answer: a)
376.8 cm3A cube is inscribed in a sphere of radius . What is the ratio of the surface area of the cube to that of the sphere?
a) 1:2
b) 1:3
c) 6:4
d) 3:2
Answer: b) 1:3
The height and radius of a cone are both doubled. By what factor does its volume increase?
a) 2
b) 4
c) 6
d) 8
Answer: d) 8
A cylinder has a height of 20 cm and radius of 7 cm. A cone is carved out from it with the same radius and height. Find the volume of the remaining solid. Use
π=227
a)
3080 cm3b)
3140 cm3c)
3300 cm3d)
3020 cm3Answer: a)
3080 cm3A hemispherical bowl has a diameter of 14 cm. Find the cost of painting its inner surface at
per square cm. Use
π=227\pi = \frac{22}{7}
a) ₹770
b) ₹1078
c) ₹800
d) ₹980
Answer: a) ₹770
A sphere is melted to form 8 smaller spheres of equal radii. What is the ratio of the radius of the original sphere to that of a smaller sphere?
a) 1:2
b) 1:3
c) 1:4
d) 1:8
Answer: b) 1:2
A cylinder is inscribed in a sphere of radius r. What is the ratio of the volume of the cylinder to that of the sphere?
a) 1:2
b) 1:3
c) 2:3
d) 1:4
Answer: c) 2:3
A hemisphere is surmounted on a cone of equal radius. If the height of the cone is equal to twice the radius, find the ratio of their volumes.
a) 1:2
b) 1:3
c) 2:3
d) 1:4
Answer: c) 2:3
What is the volume of a cube with edge length ?
a)
25 cm3b)
50 cm3c)
100 cm3d)
125 cm3Answer: d)
125 cm3The formula for the curved surface area of a cylinder is:
a)
b)
πr2hc)
πr2d)
2πr2hAnswer: a)
2πrhIf the diameter of a sphere is 14 cm, what is its radius?
a) 7 cm
b) 14 cm
c) 21 cm
d) 28 cm
Answer: a) 7 cm
The total surface area of a hemisphere is given by:
a)
b)
3πr2c)
4πr2d)
πr2Answer: b)
3πr2Which shape has the largest volume for a given surface area?
a) Cube
b) Sphere
c) Cylinder
d) Cone
Answer: b) Sphere
A cylinder has a height of 14 cm and radius 7 cm. What is its total surface area? Use
π=227
a)
462 cm2b)
616 cm2c)
968 cm2d)
1436 cm21436 \, \text{cm}^2Answer: c)
968 cm2A hollow hemisphere has an external radius of 7 cm and an internal radius of 5 cm. Find the volume of the material used. Use
π=227
a)
154 cm3b)
462 cm3c)
616 cm3d)
770 cm3Answer: c)
616 cm3A cone has a base radius of 4 cm and height 3 cm. Find its slant height.
a) 4 cm
b) 5 cm
c) 6 cm
d) 7 cm
Answer: b) 5 cm
A cone has a height of 12 cm and a base radius of 5 cm. What is its total surface area? Use
π=3.14
a)
226.2 cm2b)
188.4 cm2c)
157 cm2d)
314 cm2Answer: a)
226.2 cm2A solid sphere is melted and recast into 64 smaller spheres of equal size. If the radius of the smaller sphere is 2 cm, find the radius of the original sphere.
a) 8 cm
b) 10 cm
c) 12 cm
d) 16 cm
Answer: a) 8 cm
A cylindrical tank has a radius of 5 m and height 14 m. Find its capacity in liters. Use
π=227\pi = \frac{22}{7}
and
1 m3=1000 liters
a) 2200 liters
b) 11000 liters
c) 55000 liters
d) 22000 liters
Answer: d) 22000 liters
A hemispherical bowl of radius 7 cm is filled with water. If water is poured into cylindrical bottles with radius 3 cm and height 14 cm, how many bottles can be filled? Use
π=227
a) 5
b) 6
c) 7
d) 8
Answer: b) 6
A cuboidal water tank measures 6 m × 4 m × 2.5 m. Find the total cost of painting its outer surface at per
m2\text{m}^2
.
a) ₹400
b) ₹500
c) ₹600
d) ₹700
Answer: c) ₹600
A cone is inscribed in a hemisphere of radius . The height of the cone equals the radius of the hemisphere. Find the ratio of their volumes.
a)
b)
c)
d)
3:4Answer: b)
2:3A solid toy is made of a hemisphere mounted on a cylinder. If the radius of both is 3 cm and the height of the cylinder is 6 cm, find the total surface area. Use
π=227\pi = \frac{22}{7}
a)
b)
216 cm2c)
254 cm2d)
286 cm2Answer: d)
286 cm2A solid iron pole consists of a cylinder of height 7 m and radius 4 m, surmounted by a cone of height 3 m and radius 4 m. Find the total volume of the pole. Use
π=227\pi = \frac{22}{7}
a)
440 m3440 \, \text{m}^3b)
528 m3528 \, \text{m}^3c)
560 m3560 \, \text{m}^3d)
616 m3616 \, \text{m}^3Answer: b)
528 m3528 \, \text{m}^3
A tent is in the shape of a cylinder surmounted by a cone. The height of the cylindrical part is 3 m, the diameter of the base is 6 m, and the slant height of the conical part is 5 m. Find the area of the canvas used. Use
π=3.14\pi = 3.14
a)
113.04 m2113.04 \, \text{m}^2b)
150.72 m2150.72 \, \text{m}^2c)
176.58 m2176.58 \, \text{m}^2d)
188.4 m2188.4 \, \text{m}^2Answer: c)
176.58 m2176.58 \, \text{m}^2
A sphere is melted and cast into a hollow cylinder with external radius 5 cm, internal radius 4 cm, and height 7 cm. Find the radius of the sphere. Use
π=227\pi = \frac{22}{7}
a) 4 cm
b) 5 cm
c) 6 cm
d) 7 cm
Answer: b) 5 cm
A solid is made up of a hemisphere, a cylinder, and a cone of equal radius 7 cm. The height of the cone and cylinder is 10 cm each. Find the total volume of the solid. Use
π=227\pi = \frac{22}{7}
a)
2464 cm32464 \, \text{cm}^3b)
3080 cm33080 \, \text{cm}^3c)
4620 cm34620 \, \text{cm}^3d)
6160 cm36160 \, \text{cm}^3Answer: a)
2464 cm32464 \, \text{cm}^3
A medicine capsule is in the shape of a cylinder with hemispherical ends. If the length of the capsule is 14 mm and its diameter is 5 mm, find its total surface area. Use
π=227\pi = \frac{22}{7}
a)
220 mm2220 \, \text{mm}^2b)
231 mm2231 \, \text{mm}^2c)
308 mm2308 \, \text{mm}^2d)
385 mm2385 \, \text{mm}^2Answer: b)
231 mm2231 \, \text{mm}^2A hemispherical dome has a radius of 14 m. Find its total surface area. Use
a)
1846 m21846 \, \text{m}^2b)
1232 m21232 \, \text{m}^2c)
1540 m21540 \, \text{m}^2d)
1760 m21760 \, \text{m}^2Answer: b)
1232 m21232 \, \text{m}^2A solid metal sphere of radius 7 cm is melted and recast into 8 smaller spheres of equal size. Find the radius of each smaller sphere.
a) 3.5 cm
b) 4 cm
c) 3 cm
d) 2.5 cm
Answer: a) 3.5 cm
A cone has a slant height of 10 cm and a base diameter of 12 cm. Find its curved surface area. Use
π=3.14\pi = 3.14
a)
360 cm2360 \, \text{cm}^2b)
376.8 cm2376.8 \, \text{cm}^2c)
420 cm2420 \, \text{cm}^2d)
314 cm2314 \, \text{cm}^2Answer: a)
360 cm2A cube has a total surface area of 96
cm2\text{cm}^2
Find its volume.
a)
b)
72 cm3c)
48 cm3d)
27 cm3Answer: a)
64 cm3The slant height of a cone is 13 cm, and its height is 12 cm. Find the radius of the cone.
a) 3 cm
b) 4 cm
c) 5 cm
d) 6 cm
Answer: c) 5 cm
A spherical balloon is being inflated. If the radius increases from 7 cm to 14 cm, by what factor does the surface area increase?
a) 2
b) 4
c) 6
d) 8
Answer: b) 4
A cylinder has a height of 10 cm and radius 7 cm. If the top and bottom are open, find the surface area. Use
π=227
a)
440 cm2440 \, \text{cm}^2b)
528 cm2528 \, \text{cm}^2c)
308 cm2308 \, \text{cm}^2d)
704 cm2704 \, \text{cm}^2Answer: b)
528 cm2528 \, \text{cm}^2
A cuboid has dimensions 8 cm × 6 cm × 4 cm. Find the length of its diagonal.
a) 8 cm
b) 9 cm
c) 10 cm
d) 12 cm
Answer: c) 10 cm
A hollow cone has a base radius of 7 cm, height of 24 cm, and slant height of 25 cm. Find the total surface area. Use
π=227\pi = \frac{22}{7}
a)
b)
550 cm2550 \, \text{cm}^2c)
770 cm2770 \, \text{cm}^2d)
924 cm2924 \, \text{cm}^2Answer: c)
770 cm2770 \, \text{cm}^2
A hemisphere has a curved surface area of
1386 cm21386 \, \text{cm}^2
Find its radius. Use
π=227\pi = \frac{22}{7}
a) 14 cm
b) 21 cm
c) 28 cm
d) 7 cm
Answer: b) 21 cm
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