Question

If each edge of a cube is doubled,

(i) how many times will its surface area increase?

(ii) how many times will its volume increase?

Answer 1

(i) Let initially the edge of the cube be l.

Initial surface area = 6l²

If each edge of the cube is doubled, then it becomes 2l.

New surface area = 6(2l)² = 24l² = 4 × 6l²

Clearly, the surface area will be increased by 4 times.

(ii) Initial volume of the cube = l³

When each edge of the cube is doubled, it becomes 2l.

New volume = (2l)³ = 8l³ = 8 × l³

Clearly, the volume of the cube will be increased by 8 times.