Chapter 12, Problem 4CR

To determine

Tofind:The total area of the right square prism.

Answer to Problem 4CR

The total area of the right square prism is equal to $558$ square units.

Explanation of Solution

Given information:

The base edge of the right square prism is equal to $9$ units and volume is $891$ cubic units.

Calculation:

Write the formula to calculate the volume of the right square prism.

• $\text{V}=a^{2}h$

Where,

• $a$ is the base edge.
• $h$ is the height.

Substitute $9$ for $a$ and $891$ for $\text{V}$ in the formula.

  $\begin{array}{c}891={\left(9\right)}^{2}h\\ h=\frac{891}{81}\\ h=11\text{units}\end{array}$

So, the height of the right square prism is equal to 11 units.

Write the formula to calculate the total area of right square prism.

  $\text{A}=2a^2+4ah$

Substitute $9$ for $a$ and $11$ for $h$ in the formula for area.

  $\begin{array}{c}\text{A}=2a^2+4ah\\ =2{\left(9\right)}^2+4\times 9\times 11\\ =2\left(81\right)+396\end{array}$

Furthersimplify.

  $\begin{array}{c}\text{A}=2\left(81\right)+396\\ =162+396\\ =558\text{square}\text{units}\end{array}$

Therefore, the total area of the right square prism is equal to $558$ square units.