Question

If each edge of a cube is doubled,

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

(ii) how many times its volume increase?

Answer 1

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

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