Chapter 12.4, Problem 11PPS

To determine

To find:The volume of the cone and estimate the answer to nearest tenth.

Answer to Problem 11PPS

The volume of the cone is $17.0i{n}^3$ .

Explanation of Solution

Given:

The figure of parallel lines and transversal line is shown below in Figure 1.

  

Figure 1

Formula used:

The formula of the volume of the cone is $V=\frac{1}{3}\pi r^{2}h$ where $r$ is the radius and $h$ is the height of the cone.

Calculation:

It can be seen from the Figure 1 that the length of the radius is 1.9in and the height of the cone is 4.5in.

Substitute 1.9 for r and 4.5 for h in the formula of the cone $V=\frac{1}{3}\pi r^{2}h$ .

  $\begin{array}{c}V=\frac{1}{3}\pi {\left(1.9\right)}^2\left(4.5\right)\\ =\frac{3.61\pi }{3}\left(4.5\right)\\ =\frac{\mathrm{11.3411...}}{3}\left(4.5\right)\\ =17.01172\end{array}$

The nearest tenth value of the volume is $17.0i{n}^3$ .

Conclusion:

Thus, the volume of the cone is $17.0i{n}^3$ .