Chapter 12.7, Problem 34SR

To determine

To find:The volume of the cone.

Answer to Problem 34SR

The volume of the cone is $96008.64{\text{ mm}}^3$

Explanation of Solution

Given: Radius of the cone is 28 mm and height is 117 mm.

Formula Used:

The volume V of a cone is $V=\frac{1}{3}B.h.$

Calculation:

Consider an ice cream cone whose radius is 28 mm and height is 117 mm.

The volume V of a cone is $V=\frac{1}{3}B.h.$

Here, $B=\pi r^2$ is the area of the circle and h is the height the cone.

The area B of the circle is $B=\pi r^2$.

Substitute $r=28\text{ mm},\text{ h=117 mm}$

  $\begin{array}{l}B=\pi r^2\\ $ =\pi {(28)}^2$=784\pi \\ \approx 784(3.14)\text{ As }\pi \approx 3.14\\ =2461.76\end{array}$

  $\text{Substitute B}\approx 2461.76\text{ and }h\text{=117 in }V=\frac{1}{3}B.h.$ Substitute

  $\begin{array}{l}V=\frac{1}{3}B.h.\\ \approx \frac{1}{3}\left(2461.76\right)117\\ =\left(2461.76\right)(39)\\ =96008.64\end{array}$

Conclusion:Hence, the volume of the cone is $96008.64{\text{ mm}}^3$ .