Chapter 12.4, Problem 34PPS

To determine

To find:

The volume of the rectangular prism.

Answer to Problem 34PPS

The volume of the rectangular prism is ${\text{576 cm}}^3$ .

Explanation of Solution

Given information:

Surface arae of $432$ square inches a height of $6$ inches and a width of $12$ inches.

Calculation:

Apply the surface area formula to find the length of the base of the prism.

Assume that the length of the prism is $l$ .

Surface area formula is as follows:

  $S=Ph+2B$ , where $P$ is the perimeter and $B$ is the area of the rectangle.

Substitute $S=432$ , $P=2\left(l+12\right)6$ and $B=2\left(l\right)\left(12\right)$ in the above formula:

  $\begin{array}{c}432=2\left(l+12\right)\left(6\right)+2\left(l\right)\left(12\right)\\ 432=12l+144+24l\\ 432=36l+144\\ 36l=432-144\\ 36l=288\\ l=\frac{288}{36}\\ =8\end{array}$

Therefore, the length of the base of the prism is $8$ centimeters.

Volume of the rectangular prism is:

  $\begin{array}{c}V=Bh\\ =lwh\\ =\left(8\right)\left(12\right)\left(6\right)\\ =576{\text{ cm}}^3\end{array}$

Hence the volume of the rectangular prism is ${\text{576 cm}}^3$ .