Chapter 12.5, Problem 17PPS

To determine

To find the volume of the given cone.

Answer to Problem 17PPS

  $V\approx 240$ cubic inches (approximately)

Explanation of Solution

Given:

  

  $\text{height}(h)=9$ inches, $\text{diameter}(d)=10$ inches

Formula used:

Volume of cone, $V=\frac{1}{3}Bh=\frac{1}{3}\pi r^{2}h$

where $B=\pi r^2$ is the area of the base and $h$ is the height of the cone.

  $radius=\frac{diameter}{2}$

  $\Rightarrow r=\frac{d}{2}$

Calculation:

In the given cone, diameter $=$ 10 inches

So, radius $=\frac{10}{2}$

  $\Rightarrow r=5$ inches

Now for the volume of the cone,

  $V=\frac{1}{3}Bh=\frac{1}{3}\pi r^{2}h$

Put the values of $r=5$ and $h=9$ ,

  $\Rightarrow \frac{1}{3}\times 3.14\times {(5)}^2\times 9$

  $\left[\pi =3.14\right]$

  $\Rightarrow \frac{706.5}{3}$

  $\Rightarrow V\approx 240$ cubic inches

Conclusion:

Therefore, the volume of the given cone is $240$ cubic inches (approximately).