SURFACE AREA AND VOLUME OF A CUBE WORKSHEET

Problem 1 :

The volume of the cube is 125 dm³. Find its side.

Solution :

Volume of cube  =  125 dm³

a³  =  125

a³  =  5³

a  =  5 dm

So, the side length of cube is 5 dm.

Problem 2 :

A container is in the shape of a cube of side 20 cm. How much sugar can it hold?

Solution :

In order to find the quantity of sugar that the container can hold, we have to find the volume of container.

Side length of cubical container  =  20 cm

Volume of container  =  a³

  =  (20)³

  =  8000 cm³

Problem 3 :

A cubical tank can hold 64,000 liters of water. Find the length of the side of the tank.

Solution :

Let a be the side of the cubical tank. Volume of the tank is 27,000 litres. So,

V  =  a³  =  (27000/1000)

a³  =  27

a  =  ∛27

a  =  3 m

Problem 4 :

Three metallic cubes of side 3 cm, 4 cm and 5 cm respectively are melted and are recast into a single cube. Find the total surface area of the new cube.

Solution :

Side length of 1^st cube  =  3 cm

Side length of 2^nd cube  =  4 cm

Side length of 3^rd cube  =  5 cm

Volume of 1^st, 2^nd and 3^rd cube  =  3³ + 4³ + 5³

  =  27 + 64 + 125

  =  216

a³  =  216

a³  =  6³

a  =  6 cm

Total surface area of new cube  =  6a²

  =  6(6)²

  =  6(36)

  =  216 cm²

So, total surface area of new cube 216 cm²

Problem 5 :

Find the L.S.A, T.S.A and volume of a cube of side 5 cm.

Solution :

Lateral surface area (L.S.A)  =  4a²

  =  4(52 ) = 100 sq. cm

Total surface area (T.S.A)  = 6a²

=  6 (5² )

=  150 sq. cm

Volume of cube  =  a³

  =  5³

  =  125 cm³

Problem 6 :

Find the length of the side of a cube whose total surface area is 216 square cm.

Solution :

Let a be the side of the cube.

Given that T.S.A = 216 sq. cm

6a²  =  216 

a²  =  216/6 

a²  =  36

a  =  √36

a  =  6 cm

Problem 7 :

A cube has a total surface area of 384 sq. cm. Find its volume.

Solution :

Let a be the side of the cube. Given that T.S.A = 384 sq. cm

6a² = 384

a²  =  384/6

a²  =  64

a  =  √64  =  8 cm

Hence, volume = a³ = 8³ = 512 cm³

Problem 8 :

If the lateral surface area of a cube is 900 cm², find the length of its side.

Solution :

Lateral surface area of cube  =  4a²

4a²  =  900

a²  =  900/4

a²  =  225

a  =  √225

a  =  15 cm

Hence the side of cube is 15 cm. 

Problem 9 :

A cube has an edge length of 4 inches. You double the edge lengths. How many times greater is the volume of the new cube?

Solution :

Side length of cube = 4 inches

Doubling the side length, the new side length will be = 8 inches

Volume of old cube = 4³

= 64 cubic inches

Volume of new cube = 8³

= 512 cubic inches

Number of times = 512/64

= 8 times

So, volume of new cube is 8 times greater than volume of old cube.

Problem 10 :

Find the surface area of a cube with edge lengths of 9 centimeters.

Solution :

Side length of cube = 9 cm

Surface area = 6a²

= 6(9)²

= 6(81)

= 486 cm²

So, the total surface area of the cube is 486 cm²

Problem 11 :

How many 3/4 -centimeter cubes do you need to create a cube with an edge length of 12 centimeters?

Solution :

Volume of cube whose side length of 12 cm

= 12³

= 1728 cm³

Volume of cube which has the side length of 3/4 cm 

= (3/4)³

= 27/64 cm³

Number of cubes needed = 1728 / (27/64)

= 1728 x (64/27)

= 4096 

Problem 12 :

A keychain-sized puzzle cube is made up of small cubes. Each small cube has a surface area of 1.5 square inches.

a. What is the side length of each small cube?

b. What is the surface area of the entire puzzle cube?

Solution :

a)

Surface area of cube = 1.5 square inches

6a² = 1.5

a² = 1.5/6

a² = 0.25

a = 0.5 cm

b)

Side length of small cube = 3(1.5) ==> 4.5 cm

Surface area of cube (or) keychain = 6a²

= 6(4.5)²

= 6(20.25)

= 121.5 square inches

Problem 13 :

To finish a project, you need to paint the lateral surfaces of a cube with side length 2.5 inches. Find the area that you need to paint.

Solution :

Side length = 2.5 inches

Lateral surface area of cube = 4a²

= 4(2.5)²

= 4(6.25)

= 25 square inches

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.