Q44. - Algebra 1

Question

Find the volume and surface area of each rectangular prism give the measurement below.

$l=3cm,w=1cm,h=3cm$

Step-by-Step Solution

Answer

$\begin{array}{l}\text{Volume of the prism is }9{\text{ cm}}^3\\ \text{Surface area of rectangular prism is }30{\text{ cm}}^2\end{array}$

Step 1. The formula of the volume and surface area of the rectangular prism.

$\begin{array}{l}\text{Volume }V=lwh\\ \text{Surface area }A=2\left(lw+wh+hl\right)\end{array}$

Step 2. Calculate the volume.

$\begin{array}{l}V=\left(3\right)\left(1\right)\left(3\right)\\ V=9{\text{ cm}}^3\end{array}$

Step 3. Calculate the surface area.

$\begin{array}{l}A=2\left[\left(3\right)\left(1\right)+\left(1\right)\left(3\right)+\left(3\right)\left(3\right)\right]\\ A=2\left(3+3+9\right)\\ A=30{\text{ cm}}^2\end{array}$

Therefore, the volume and surface area of a rectangular prism.

$\begin{array}{l}V=9{\text{ cm}}^3\\ A=30{\text{ cm}}^2\end{array}$