Chapter 9, Problem 2P

Solution

To determine the area of the base of the prism.

The given solution is full credit solution.

Given:

The dimensions of the prism are shown below:

  

Calculation:

First, the side lengths b and $h$ using trigonometric functions are calculated as:

  $\begin{array}{l}\sin \theta =\frac{b}{30}\\ b=30\times \sin {67}^{°}\\ b=30\times 0.9205\\ b=27.62\end{array}$

And,

  $\begin{array}{l}\cos \theta =\frac{h}{30}\\ h=30\times \cos {67}^{°}\\ h=30\times 0.3907\\ h=11.72\end{array}$

Then the area of the base is calculated as:

  $\begin{array}{l}\text{Area}=\frac{1}{2}bh\\ A=\frac{1}{2}\times 27.62\times 11.72\\ A=161.9c{m}^2\end{array}$

And the volume of the prism is calculated as:

  $\begin{array}{l}\text{Volume = Area of base}\times \text{ height}\\ V=161.9\times 6\\ V=971.4c{m}^3\end{array}$

Here, all the steps for the given solution are correct. The first step is to calculate the area of triangle. Then, to find the volume of the prism, the triangular area will be multiplied by the height of the prism. Hence, the given solution is correct and deserves full credit.