Chapter 12.5, Problem 20PSC

To determine

To find: The volume of frustum shown in the figure.

Answer to Problem 20PSC

The volume is $716.571{\text{ units}}^3$

Explanation of Solution

Given info:

  

  $\begin{array}{l}r=6units\\ R=9units\\ l=5units\end{array}$

Formula used:

  $l=\sqrt{{(R-r)}^2+h^2}$

  $V=\frac{\pi }{3}h(R^2+r^2+R.r)$$$

Calculation:

Substituting given values of h, R, r into formula of l

  $\begin{array}{l}5=\sqrt{{(9-6)}^2+{(h)}^2}\\ h^2=25-16\\ h=4units\end{array}$

Now putting this value into formula of Volume (V)

  $\begin{array}{l}V=\frac{\pi }{3}\times 4\times (81+36+54)\\ V=\frac{3.14}{3}\times 4\times 171\\ V=716.571{(}^u\end{array}$

Conclusion:

Hence Volume, $V=716.571{\text{ units}}^3$