Chapter 12.4, Problem 24PPS

To determine

To find:

The volume of the solid figure.

Answer to Problem 24PPS

The volume of the solid figure is $48.9{\text{ m}}^3$ .

Explanation of Solution

Given information:

  

Calculation:

The circular base at the top and bottom is a cylinder.

The middle piece is in the form of rectangle, then the prism would be right.

Since, the middle piece is a parallelogram, it is oblique.

The radius is $1.8\text{ m}$ , the height is $4.8\text{ m}$ , and the slant height is $\text{6 m}$ .

So, if the two solids have the same height and the same cross-sectional area at every level then they have the same volume.

So, the volume of a right prism and an oblique one of the same height and cross-sectional area are same.

Therefore, the volume is:

  $\begin{array}{c}V=Bh\\ =\pi r^{2}h\\ =\pi {\left(1.8\right)}^2\left(4.8\right)\\ \approx 48.9{\text{ m}}^3\end{array}$

Hence, the volume of the solid figure is $48.9{\text{ m}}^3$ .