Question

If each edge of a cube is doubled :
1) how many times will its surface area increases?
2) how many times will its volume increase? ​

Answer 1

Let the initial edge of the cube be 'l' cm.

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

(i) Initial surface area = 6 l²

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

Ratio = 6 l² : 24 l² = 1:4

Thus, the surface are increases by 4 times

(ii) Initial volume of the cube = l³

New volume = (2l)³ = 8 × l³

Ratio = l³: 8 l³= 1:8

Thus, the volume increases by 8 times.