Chapter 12.2, Problem 22PPS

To determine

The volume value of the each figure:

  

Answer to Problem 22PPS

The volume of the figure is $168c{m}^3$ .

Explanation of Solution

Given:

  

  $\begin{array}{l}{l}_1=l_2=l_3=7cm\\ b_1=b_2=3cm\\ h_1=h_2=h_3=3cm\\ w_3=5cm\end{array}$

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 two triangular prism and one rectangular prism so number each volume as:

  

Volume of triangular prism 1:

  $\begin{array}{l}{V}_1=\frac{1}{2}\left(l_1\times b_1\times h_1\right)\\ V_1=\frac{1}{2}\left(7\times 3\times 3\right)\\ V_1=31.5c{m}^3\end{array}$

Volume of triangular prism 2 is same as Volume of triangular prism 1:

  $V_2=V_1=31.5c{m}^3$

Volume of rectangular prism 3:

  $\begin{array}{l}{V}_3=l_3\times w_3\times h_3\\ V_3=7\times 5\times 3\\ V_3=105c{m}^3\end{array}$

So, total volume of the figure is:

  $\begin{array}{l}V=V_1+V_2+V_3\\ V=31.5c{m}^3+31.5c{m}^3+105c{m}^3\\ V=168c{m}^3\end{array}$

Conclusion:

Hence, the volume of the prism is $168c{m}^3$