Class 9 Practice – Level 2 – Set 1 - Surface Areas and Volumes

Total questions: 25

A cylindrical water tank has a radius of 5 m and the height of 20 m . if the tank is open at the top , what is the surface area that needs to be painted?

Topic: Surface Area of Cylinders

$ \displaystyle 200\pi \text{ }{{\text{m}}^{2}}$

$ \displaystyle 250\pi \text{ }{{\text{m}}^{2}}$

$ \displaystyle 300\pi \text{ }{{\text{m}}^{2}}$

$ \displaystyle 350\pi \text{ }{{\text{m}}^{2}}$

None

A cone has a base radius of 7 cm and a slant height of 25 cm. if the height of the cone is 24 cm , what is its volume?

Topic: Volume of Cones

$ \displaystyle 343\pi \text{ c}{{\text{m}}^{3}}$

$ \displaystyle 616\pi \text{ c}{{\text{m}}^{3}}$

$ \displaystyle 784\pi \text{ c}{{\text{m}}^{3}}$

$ \displaystyle 1029\pi \text{ c}{{\text{m}}^{3}}$

None

The surface area of a sphere is $ \displaystyle 616\text{ c}{{\text{m}}^{2}}$. what is the radius of the sphere?

Topic: Surface Area of Spheres

7 cm

8 cm

9 cm

10 cm

None

A solid sphere has a diameter of 14 cm . if the sphere is melted and recast into smaller spheres, each of radius 2 cm, how many smaller spheres can be made?

Topic: Volume of Spheres

125

216

None

A conical tent has a slant height of 13 m and a base diameter of 10 m . what is the area of the canvas required to make the tent?

Topic: Surface Area of Cones

$ \displaystyle 65\pi \text{ }{{\text{m}}^{2}}$

$ \displaystyle 80\pi \text{ }{{\text{m}}^{2}}$

$ \displaystyle 120\pi \text{ }{{\text{m}}^{2}}$

$ \displaystyle 130\pi \text{ }{{\text{m}}^{2}}$

None

A cuboid has a length of 8 m, a breadth of 6 m, and the height of 4 m. if $ \displaystyle \dfrac{2}{3}$ of the cuboid is filled with water , what is the volume of the water is the cuboid?

Topic: Volume of Cylinders

$ \displaystyle 64\text{ }{{\text{m}}^{3}}$

$ \displaystyle 96\text{ }{{\text{m}}^{3}}$

$ \displaystyle 128\text{ }{{\text{m}}^{3}}$

$ \displaystyle 160\text{ }{{\text{m}}^{3}}$

None

A spherical balloon is being inflated and its radius increases from 7 cm to 14 cm. what is the increase in the surface area of the balloon?

Topic: Surface Area of Spheres

$ \displaystyle 308\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 616\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 924\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 1232\pi \text{ c}{{\text{m}}^{2}}$

None

The height of cone is three times its base radius . if the volume of the cone is $\displaystyle 48\pi \text{ c}{{\text{m}}^{3}}$ ,what is the height of the cone?

Topic: Volume of Cones

4 cm

6 cm

8 cm

12 cm

None

A hollow hemisphere is painted on both the inner and outer surfaces. If the thickness of the hemisphere is 1 cm and the inner radius is 6 cm , what is the total surface area painted?

Topic: Surface Area of Hemispheres

$ \displaystyle 264\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 396\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 528\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 660\pi \text{ c}{{\text{m}}^{2}}$

None

10.

A cylindrical container has a height of 15 cm and a radius of 7 cm . If the container is filled with water at a rate of $ \displaystyle 5\text{ c}{{\text{m}}^{3}}$ per second, how long will it take to fill the container?

Topic: Surface Area of Cylinders

462 seconds

924 seconds

1386 seconds

1580 seconds

None

11.

A conical vessel with a radius of 4 cm and height of 8 cm is to be completely covered with a plastic sheet. What is the area of the plastic sheet required?

Topic: Surface Area of Cones

$ \displaystyle 25\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 40\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 45\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 60\pi \text{ c}{{\text{m}}^{2}}$

None

12.

A spherical ball of diameter 14 cm is melted and recast into 8 smaller balls of equal size. What is the diameter of each smaller ball?

Topic: Volume of Spheres

7 cm

5 cm

3.5 cm

2 cm

None

13.

A cuboid with dimensions $ \displaystyle \text{10 cm }\times \text{5 cm }\times \text{3 cm}$ is painted on all six faces .What is the total area painted?

Topic: Surface Area of Cuboids

$\displaystyle \text{130 c}{{\text{m}}^{2}}$

$\displaystyle \text{150 c}{{\text{m}}^{2}}$

$\displaystyle \text{160 c}{{\text{m}}^{2}}$

$\displaystyle \text{170 c}{{\text{m}}^{2}}$

None

14.

A cone with a height of 9 cm and base radius of 5 cm is partially filled with water. If the water height is 6 cm , what is the volume of water in the cone?

Topic: Volume of Cones

$ \displaystyle 100\pi \text{ c}{{\text{m}}^{3}}$

$ \displaystyle 150\pi \text{ c}{{\text{m}}^{3}}$

$ \displaystyle 200\pi \text{ c}{{\text{m}}^{3}}$

$ \displaystyle 250\pi \text{ c}{{\text{m}}^{3}}$

None

15.

A sphere is cut into two equal hemispheres. What is the increase in the total surface area?

Topic: Surface Area of Spheres

$ \displaystyle 2\pi {{r}^{2}}$

$ \displaystyle 4\pi {{r}^{2}}$

$ \displaystyle 6\pi {{r}^{2}}$

$ \displaystyle 8\pi {{r}^{2}}$

None

16.

A cylindrical drum with a height of 1.5 m and a diameter of 1 m is filled with sand. What is the volume of the sand in the drum?

Topic: Volume of Cylinders

$ \displaystyle \text{1}\text{.178 }{{\text{m}}^{3}}$

$ \displaystyle \text{1}\text{.5 }{{\text{m}}^{3}}$

$ \displaystyle \text{2}\text{.178 }{{\text{m}}^{3}}$

$ \displaystyle \text{2}\text{.356 }{{\text{m}}^{3}}$

None

17.

A hallow metal hemisphere has an inner radius of 10 cm and an outer radius of 12 cm. what is the area of the metal used?

Topic: Surface Area of Hemispheres

$ \displaystyle 132\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 264\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 396\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 528\pi \text{ c}{{\text{m}}^{2}}$

None

18.

A cone has a slant height of 13 cm and base radius of 5 cm. If the height of the cone is 12 cm , what is the volume of the cone?

Topic: Volume of Cones

$ \displaystyle 100\pi \text{ c}{{\text{m}}^{3}}$

$ \displaystyle 300\pi \text{ c}{{\text{m}}^{3}}$

$ \displaystyle 400\pi \text{ c}{{\text{m}}^{3}}$

$ \displaystyle 500\pi \text{ c}{{\text{m}}^{3}}$

None

19.

A cylindrical can has a radius of 7 cm and height of 15 cm . What is the area of the metal sheet required to make the can, including the top and bottom?

Topic: Surface Area of Cylinders

$ \displaystyle 968\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 858\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 772\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 616\pi \text{ c}{{\text{m}}^{2}}$

None

20.

A solid metal sphere of radius 6 cm is melted and recast into 8 identical spheres. What is the radius of each smaller sphere?

Topic: Volume of Spheres

3 cm

4 cm

5 cm

6 cm

None

21.

A hemisphere has a diameter of 20 cm , if the outer surface is to be painted , what is the area that needs to be painted?

Topic: Surface Area of Hemispheres

$ \displaystyle 200\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 400\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 500\pi \text{ c}{{\text{m}}^{2}}$

$ \displaystyle 600\pi \text{ c}{{\text{m}}^{2}}$

None

22.

A cone has a base radius 3 cm and height of 4 cm , if the cone is melted and recast into a cylinder of the same base radius, what is the height of the cylinder?

Topic: Volume of Cones

1 cm

2 cm

3 cm

4 cm

None

23.

A cuboid with dimension $ \displaystyle \text{10 cm }\times \text{8 cm }\times \text{6 cm}$ is to be wrapped in the gift paper. what is the minimum area of the gift paper to wrap the cuboid completely?

Topic: Surface Area of Cuboids

$ \displaystyle \text{248 c}{{\text{m}}^{2}}$

$ \displaystyle \text{268 c}{{\text{m}}^{2}}$

$ \displaystyle \text{376 c}{{\text{m}}^{2}}$

$ \displaystyle \text{308 c}{{\text{m}}^{2}}$

None

24.

A sphere has a radius of 14 cm , if a cube is inscribed in the sphere , what is the volume of the cube?

Topic: Volume of Spheres

$ \displaystyle \text{1372 c}{{\text{m}}^{3}}$

$ \displaystyle \text{2197 c}{{\text{m}}^{3}}$

$ \displaystyle \text{2744 c}{{\text{m}}^{3}}$

$ \displaystyle \text{3430 c}{{\text{m}}^{3}}$

None

25.

A hallow hemisphere has an inner radius of 7 cm and an outer radius of 9 cm , what is the volume of the material used to make the hemisphere?

Topic: Surface Area of Hemispheres

$\displaystyle 936\pi \text{ c}{{\text{m}}^{3}}$

$\displaystyle 1056\pi \text{ c}{{\text{m}}^{3}}$

$\displaystyle 1184\pi \text{ c}{{\text{m}}^{3}}$

$\displaystyle 1232\pi \text{ c}{{\text{m}}^{3}}$

None

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Class 9 Practice – Level 2 – Set 1 - Surface Areas and Volumes

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