Question

If each edge of a cube is doubled, how many times will its surface area increase?

Answer 1

Step 1: Calculate surface area of cube when the edge is doubled.

The Surface area of a cube is given by multiplying the square of edge by $6$.

Surface area of cube$=6s^2$.

When the edge is doubled it $s$ becomes $2s$.

Now, the surface area of cube is,

$\begin{array}{cl}6{\left(2s\right)}^2=& 6\left(4s^2\right)\\ =& 24s^2\end{array}$

Step 2: Find the ratio between the surface area of the original edge and doubled edge.

Surface area of original cube is $6s^2$.

Surface area of cube with doubled edge is $24s^2$.

Ratio between the surface areas $=6:24=1:4$

Therefore, the surface area of the cube will increase $4$ times if the edge is doubled.