SURFACE AREA AND VOLUME OF A CUBE WORKSHEET

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

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

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

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.

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

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

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

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

1. Answer :

Volume of cube  =  125 dm³

a³  =  125

a³  =  5³

a  =  5 dm

So, the side length of cube is 5 dm.

2. Answer :

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

3. Answer :

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

4. Answer :

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

5. Answer :

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

6. Answer :

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

7. Answer :

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

8. Answer :

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. 

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