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CBSE - Class 9 Mathematics Surface Area and Volumes Worksheet

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π = 3.14).

The volumes of the two spheres are in the ratio 64 : 27. Find the ratio of their radii.

a. 16:9 b. 4:3 c. 2:3 d. 4:9

Fill in the blanks: The surface of a sphere of diameter 14 cm in sq. cm is _______.

a. 616 b. 560 c. 1232 d. 456

Curved surface area of a right circular cylinder is 2.2 sq. m. If the diameter of the base of the cylinder is 0.7 m, find its height.

a. 0.5 m b. 2 m c. 1 m d. 0.25 m

Find the surface area of a sphere of diameter: (i) $14$ cm

Diagonal of a cube measures 4√3 cm. Find its volume?

a. 8 cu cm b. 27 cu cm c. 16 cu cm d. 64 cu cm

In a hot water heating system, there is a cylindrical pipe of length 35m and diameter 10 cm. Find its total radiating surface?

a. 11 sq m b. 22 sq m c. 44 sq m d. None of these

The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of 10 per m² is 15000, find the height of the hall

The volume of a right circular cone is $9856$ cm$^3$. If the diameter of the base is $28$ cm, find (ii) slant height of the cone

10.

A heap of wheat is in the form of a cone whose diameter is $10.5$ m and height is $3$ m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

11.

Radius and depth of a conical pit are 1.75 m and 12 m respectively. Find its capacity in kiloliters.

a. 32.5 kl b. 38.5 kl c. 42.5 kl d. None of these

12.

The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?

13.

A solid cylinder is melted and casted into a cone of same radius. Find the ratio of their heights?

a. 3:2 b. 1:3 c. 1:2 d. 1:6

14.

Voulme of a cube is 343 cm³. Find its total surface area?

a. 294 sq cm b. 196 sq cm c. 512 sq cm d. 49 sq cm

15.

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

16.

The radius of a metallic spherical ball is 3cm. It is melted and recast into spherical balls each of radius 0.75cm. Find the number of small balls so formed.

a. 16 b. 24 c. 64 d. 32

17.

Fill in the blanks: Radius of a cricket ball is four times than that of a table tennis ball. The ratio of their volume is _______.

a. 4:1 b. 1:4 c. 64:1 d. 16:1

18.

Find the radius of a sphere whose surface area is $154$ cm$^2$.

19.

Diagonal of a cube measures 9√3 cm. Find its total surface area?

20.

Three metal cubes whose edge measure 3cm, 4cm and 5cm respectively are melted to form a single cube, find its edge.

a. 5 cm b. 7 cm c. 6 cm d. 4 cm

Worksheet Answers

Option A

Option B

Option A

Option C

Option D

Option A

Option B

11.

Option B

12.

0.4375

13.

Option B

14.

Option A

16.

Option C

17.

Option C

19.

486 sq cm

20.

Option C

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