Chapter 12.2, Problem 17PPS

To determine

Thetotal volume of blocks by using the following figure:

Answer to Problem 17PPS

The total volume of blocks is $11664i{n}^3$ .

Explanation of Solution

Given:

  $\begin{array}{l}l=18in\\ w=18in\\ h_1=6in\end{array}$

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 given by the following expression:

  $V=l\times w\times h$

Volume of 3:

  $\begin{array}{l}{V}_1=l\times w\times h_1\\ V_1=18\times 18\times 6\\ V_1=1944i{n}^3\end{array}$

Volume of 2:

  $\begin{array}{l}{V}_2=l\times w\times h_2\\ V_2=18\times 18\times \left(6+6\right)\\ V_2=3888i{n}^3\end{array}$

Volume of 3:

  $\begin{array}{l}{V}_3=l\times w\times h_3\\ V_3=18\times 18\times \left(6+6+6\right)\\ V_3=5832i{n}^3\end{array}$

So, the total blocks volume is calculated as:

  $\begin{array}{l}V=V_1+V_2+V_3\\ V=1944i{n}^3+3888i{n}^3+5832i{n}^3\\ V=11664i{n}^3\end{array}$

Conclusion:

Hence, the total blocks volume is $11664i{n}^3$ .