Chapter 12.2, Problem 16PPS

To determine

Thevolume of dog house by using the following figure:

Answer to Problem 16PPS

The height of the dog houseis $27,300i{n}^3$ .

Explanation of Solution

Given:

  $\begin{array}{l}L=l=35in\\ B=w=30in\\ H=12in\\ h=20in\end{array}$

Concept Used:

The volume of the triangular prism is given by the following expression:

  $V=\frac{1}{2}\left(L\times B\times H\right)$

Where,

Length of triangular prism: $L$

Base of triangular prism: $B$

Height of triangular prism: $H$

The volume of the rectangular prism is given by the following expression:

  $V=l\times w\times h$

Where,

Length of rectangular prism: $l$

Width of rectangular prism: $w$

Height of rectangular prism: $h$

Calculation:

The volume of the triangular prism is calculated by using the follwoing formula:

  $V_1=\frac{1}{2}\left(L\times B\times H\right)$

Put the given values:

  $\begin{array}{l}{V}_1=\frac{1}{2}\left(L\times B\times H\right)\\ V_1=\frac{1}{2}\left(35\times 30\times 12\right)\\ V_1=6300i{n}^3\end{array}$

The volume of the rectangular prism is given by the following expression:

  $V_2=l\times w\times h$

Put the given values:

  $\begin{array}{l}{V}_2=l\times w\times h\\ V_2=35\times 30\times 20\\ V_2=21000i{n}^3\end{array}$

So, the total volume of dog house is calculated as:

  $\begin{array}{l}V=V_1+V_2\\ V=6300i{n}^3+21000i{n}^3\\ V=27,300i{n}^3\end{array}$

Conclusion:

Hence, the volume of the dog houseis $27,300i{n}^3$ .