Chapter 12.5, Problem 8CYU

To determine

To find the volume of the given cone.

Answer to Problem 8CYU

  $V=4,710$ cubic meters

Explanation of Solution

Given:

  

Slant height ( $l$ ) $=25$ meters, radius $=15$ meters

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.

Pythagoras Theorem:

In right angle $\Delta ABC$

  $A{B}^2+B{C}^2=A{C}^2$

Calculation:

  

In right angled $\Delta ABC$,$A{B}^2+B{C}^2=A{C}^2$

Now putting the values,

  $\Rightarrow A{B}^2+{15}^2={25}^2$

  $\Rightarrow A{B}^2={25}^2-{15}^2$

  $\Rightarrow A{B}^2=625-225$

  $\Rightarrow A{B}^2=400$

  $\Rightarrow AB=\sqrt{400}$

  $\Rightarrow AB=h=20$ meters

For the volume ( $V$ ) of the cone,

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

Put the values of $r=4.2$ and $h=7.3$ ,

  $\Rightarrow \frac{1}{3}\times 3.14\times {(15)}^2\times 20$

  $\left[\pi =3.14\right]$

  $\Rightarrow \frac{14130}{3}$

  $\Rightarrow V=4,710$ cubic meters

Conclusion:

Therefore, the volume of the given cone is $4,710$ cubic meters.