Question

If side of a cube is doubled then
i) How many times its surface area will increase?
ii) How many times its volume will increase?

Answer 1

Let initial side be a.

$\Rightarrow$ Initial surface area, $S_1=6a^2$, volume $V_1=a^3$

$a+\to 2a$

$\Rightarrow S_2=6(2a{)}^2=24a^2$, volume $V_2=(2a{)}^3=8a^3$

$\frac{S_2}{S_1}=\frac{24a^2}{6a^2}=4$

$\frac{V_2}{V_1}=\frac{8a^3}{a^3}=8$.