Chapter 12.2, Problem 5PPS

To determine

The volume value of the given figure on its right side from the following options:

A. $60i{n}^3$

B. $56i{n}^3$

C. $56i{n}^3$

D. $840i{n}^3$

Answer to Problem 5PPS

The correct option is B. The volume of figure is $552i{n}^3$ .

Explanation of Solution

Given:

  $\begin{array}{l}{l}_1=2in\\ l_2=8in\\ l_3=10in\\ w_1=2in\\ w_2=4in\\ w_3=6in\\ h_1=2in\\ h_2=4in\\ h_3=4in\end{array}$

Concept Used:

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

  $V=l\times w\times h$

Where,

Length of prism: $l$

Widthof prism: $w$

Height of prism: $h$

Calculation:

The volume of the prism iscalculated by using the follwoing formula:

  $V=l\times w\times h$

Now, need to number the area of the prism to calcualte the total volume at the right side:

Volumeof $1$ :

  $\begin{array}{l}{V}_1=l_1{w}_1{h}_1\\ V_1=2\times 2\times 2\\ V_1=8i{n}^3\end{array}$

Volumeof $2$ :

  $\begin{array}{l}{V}_2=l_2{w}_2{h}_2\\ V_2=6\times 6\times 4\\ V_2=144i{n}^3\end{array}$

Volumeof $3$ :

  $\begin{array}{l}{V}_3=l_3{w}_3{h}_3\\ V_3=10\times 10\times 4\\ V_3=400i{n}^3\end{array}$

So, the total volume of prism at teh right side:

  $\begin{array}{l}V=V_1+V_2+V_3\\ V=8+144+400\\ V=552i{n}^3\end{array}$

Conclusion:

Hence, the volume of the prism is $552i{n}^3$ .