Chapter 12.2, Problem 4GP

To determine

The volume value of the the rectangular prism on its right side from the following options:

F. $60c{m}^3$

G. $73.5c{m}^3$

H. $98c{m}^3$

J. $107.5c{m}^3$

Answer to Problem 4GP

The correct option is G. The volume of the rectangular prism is $73.5c{m}^3$ .

Explanation of Solution

Given:

  $\begin{array}{l}{l}_1=l_2=7cm\\ w_1=4cm\\ w_2=2.5cm\\ h_1=1cm\\ h_2=2cm\end{array}$

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: $h$

Calculation:

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

  $V=l\times w\times h$

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

Volume of $1$ rectangualr prism:

  $\begin{array}{l}{V}_1=l_1{w}_1{h}_1\\ V_1=7\times 2.5\times 1\\ V_1=17.5c{m}^3\end{array}$

Volume of $2$ rectangualr prism:

  $\begin{array}{l}{V}_2=l_2{w}_2{h}_2\\ V_2=7\times 4\times 2\\ V_2=56c{m}^3\end{array}$

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

  $\begin{array}{l}V=V_1+V_2\\ V=17.5+56\\ V=73.5c{m}^3\end{array}$

Conclusion:

Hence, the volume of the rectangular prism is $73.5c{m}^3$ .