Chapter 12.4, Problem 23PPS

To determine

To find:

The volume of the solid figure.

Answer to Problem 23PPS

The volume of the solid figure is $3934.9{\text{ cm}}^3$ .

Explanation of Solution

Given information:

  

Calculation:

Apply the Pythagorean theorem to find the height of the base.

One leg of the base is $\text{14 cm}$ and the hypotenuse is $\text{31}\text{.4 cm}$ .

  $\begin{array}{c}{a}^2+b^2=c^2\\ {14}^2+b^2={\left(31.4\right)}^2\\ b^2={\left(31.4\right)}^2-{14}^2\\ b=\sqrt{{\left(31.4\right)}^2-{14}^2}\\ =\sqrt{789.96}\\ \approx 28.1\end{array}$

Also, the height of the prism is $20\text{ cm}$ .

The volume of a prism is $V=Bh$ .

  $\begin{array}{c}V=\frac{1}{2}\left(14\right)\left(28.1\right)\left(20\right)\\ =\left(7\right)\left(28.1\right)\left(20\right)\\ \approx 3934.9{\text{ cm}}^3\end{array}$

Hence, the volume of the solid figure is $3934.9{\text{ cm}}^3$ .