Chapter 12.2, Problem 23PPS

To determine

The volume value of the each figure:

  

Answer to Problem 23PPS

The volume of the figure is $154f{t}^3$ .

Explanation of Solution

Given:

  

  $\begin{array}{l}{l}_1=l_2=4ft\\ b_1=2.5ft\\ h_1=2ft\\ h_2=4ft\\ w_2=9ft\end{array}$

Concept Used:

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: $h$

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: $h$

Calculation:

In the given figure there are one triangular prism and one rectangular prism so number each volume as:

  

Valume of triangular prism 1:

  $\begin{array}{l}{V}_1=\frac{1}{2}\left(l_1\times b_1\times h_1\right)\\ V_1=\frac{1}{2}\left(4\times 2.5\times 2\right)\\ V_1=10f{t}^3\end{array}$

Volume of rectangular prism : 2

  $\begin{array}{l}{V}_2=l_2\times w_2\times h_2\\ V_2=4\times 9\times 4\\ V_2=144f{t}^3\end{array}$

So, total volume of the figure is:

  $\begin{array}{l}V=V_1+V_2+V_3\\ V=10f{t}^3+144f{t}^3\\ V=154f{t}^3\end{array}$

Conclusion:

Hence, the volume of the prism is $154f{t}^3$