Chapter 12.3, Problem 33SR

To determine

volume of given figure.

Answer to Problem 33SR

volume of given figure is $126i{n}^3$

Explanation of Solution

Given:

Length of the rectangular prism $=8in$

Height of the rectangular prism $=3in$

Width of the rectangular prism $=4in$

Length of the triangular prism $=4in$

Height of the triangular prism $=3in$

Width of the triangular prism $=5in$

Concept Used:

Volume of rectangular prism is calculated by,

  $V=LWH$

Where,

  $V=$ volume of prism.

  $W=$ width of prism.

  $h=$ height of prism.

  $L=$length of prism.

Calculation:

Volume of rectangular prism is calculated as,

  $V=LWH$

Put the given values In formula

  $\begin{array}{l}V=8\times 3\times 4\\ V=96i{n}^3\end{array}$

Thus volume of prism is $96i{n}^3$

Volume of triangular prism is calculated as,

  $V=\frac{1}{3}BH$

Put the given values In formula

  $\begin{array}{l}V=\frac{1}{2}\left(lwh\right)\\ V=\frac{1}{2}\left(4\times 5\times 3\right)\\ V=30i{n}^3\end{array}$

Thus volume of prism is $30i{n}^3$

The volume of composite given figure:

  $\begin{array}{l}=Volumeofrectangularprism+Volumeof\text{ triangular }prism\\ =96i{n}^3+30i{n}^3\\ =126i{n}^3\end{array}$

Conclusion:

Thus, volume of given figure is $126i{n}^3$