Question

A rectangular prism has a base that is $4$m by $6$m and a height of $10$ m. If all dimensions are doubled, what happens to the volume?

Answer 1

Step 1: Compute the volume of the rectangular prism with base width and length $4$ m and $6$ m and height $10$ m.

The volume of the rectangular prism is calculated by $V=lwh$, where $l$ is the length of the base, $w$ is the width of the base and $h$ is the height of the prism.

Substitute $l$ as $6$ m , $w$ as $4$m and $h$ as $10$ m in $V=lwh$ and simplify.

$$\begin{gathered} V=6\times 4\times 10 \\ \therefore V=240{\mathrm{m}}^3 \end{gathered}$$

Step 2: Compute the volume when the dimensions are doubled.

The dimensions are doubled then the length is $12$ m, width is $8$ m and the height is $20$ m

Substitute $l$ as $12$ m , $w$ as $8$m and $h$ as $20$ m in $V=lwh$ and simplify.

$$\begin{gathered} V=12\times 8\times 20 \\ \therefore V=1920m^3 \end{gathered}$$

Step 3: Compute what happens to the volume when the dimensions of the prism are doubled.

Divide the new volume by the old volume to obtain the ratio.

$\frac{1920}{240}=8$

Therefore, the volume increases $8$ times.

Hence, the volume increases $8$ times when the dimensions are doubled.