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 = 6 l 2
If each edge of the cube is doubled, then it becomes $2l.$
New surface area =$6(2l)^ 2$
$= 24 l$2
= 4 $\times$ 6 l 2
Clearly, the surface area will be increased by 4 times.

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(ii) Initial volume of the cube = l 3
When each edge of the cube is doubled, it becomes 2 l.
New volume $= (2l)^3 = 8l^ 3 = 8 \times l^ 3$
Clearly, the volume of the cube will be increased by 8 times.