Question

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

Answer 1

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

Volume of a cube is given as

$V=s^3$.

Where, $V$ is the volume and $s$ is the length of the edges of the cube.

Initially, the volume is, $V_1=s^3$

When the edge of the cube is doubled, $s$ becomes $2s$.

Now, the new volume of the cube is

$\begin{array}{rcl}{V}_2& =& {\left(2s\right)}^3\\ & \Rightarrow & V_2=8s^3\end{array}$

Step 2: Find the ratio between the volumes of both the cubes.

Volume of the original cube is $s^3$.

Volume of the cube with doubled edge is $8s^3$.

The ratio between the volumes $=s^3:8s^3=1:8$.

Therefore, the volume of the cube becomes $8$ times when the edge is doubled.