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

$\Rightarrow \left(i\right)$ Initial surface area $=6\times l\times l$
New surface area $=6\times (2\times l)\times (2\times l)=4\times$ initial surface area.
So, the new surface area will be increased by $4$ times.
$\Rightarrow \left(ii\right)$ Intial volume $=l\times l\times l$
Final volume $=\left(2l\right)\times \left(2l\right)\times \left(2l\right)=8\times$ initial volume.
So, volume of the cube will be increased by $8$ times.