Chapter 12.4, Problem 34STP

To determine

To find: height of a cone.

Answer to Problem 34STP

Height of the cone $144.68mm$

Explanation of Solution

Given:

Volume of cone $=3786m{m}^3$ .

Radius of cone $=5mm$

Concept used:

Volume of cone is calculated as,

  $V=\pi r^3\frac{h}{3}$

Where,

  $V=$ volume of cone

  $r=$ radius of cone

  $H=$ height of cone.

Volume of cone is calculated as,

  $V=\pi r^2\frac{h}{3}$

Now put the values in the equation,

  $V=\pi r^2\frac{h}{3}$

  $3786=\pi {\left(5\right)}^2\frac{h}{3}$

  $\begin{array}{l}3786=\pi \left(25\right)\frac{h}{3}\\ 3786=78.5\times \frac{h}{3}\\ h=144.68mm\end{array}$

Height of the cone $144.68mm$

Conclusion:

Thus, Height of the cone $144.68mm$.