Chapter 12.4, Problem 12PPS

To determine

The volume of pentagonal pyramid whose height and base area is $12in,52i{n}^2$ respectively.

Answer to Problem 12PPS

The volume of the pentagonal pyramid is $208i{n}^3$

Explanation of Solution

Given:

  $\begin{array}{l}h=12in\\ A=52i{n}^2\end{array}$

Concept Used:

The volume of the pentagonal pyramid is given by the following expression:

  $V=\frac{Ah}{3}$

Where,

Radius of cone: $r$

Height of cone: $h$

Calculation:

The volume of the pentagonal pyramid is given by the following expression:

  $\begin{array}{l}V=\pi r^2\frac{h}{3}\\ V=\frac{Ah}{3}\end{array}$

Where,

Base circle area: $A=B=\pi r^2$

Put the given data in eq.

  $\begin{array}{l}V=\frac{Ah}{3}\\ V=\frac{52\times 12}{3}\\ V=208i{n}^3\end{array}$

Conclusion:

Hence, the volume of the pentagonal pyramid is $208i{n}^3$