Chapter 13, Problem 31RP

To determine

To find: The volume of the solid formed.

Answer to Problem 31RP

Thevolume of the solid is $339.3$ .

Explanation of Solution

Given:

The given points are $\left(0,0\right),\left(6,0\right)$ and $\left(0,6\sqrt{3}\right)$ .

Calculation:

Consider the given points are $\left(0,0\right),\left(6,0\right)$ and $\left(0,6\sqrt{3}\right)$ .

From the given points the volume is the volume of the cone as,

  $\begin{array}{c}V=\frac{1}{3}\pi r^2{h}_1^2+\frac{1}{3}\pi r^2{h}_2^2\\ =\frac{1}{3}\pi r^2\left(h_1+h_2\right)\end{array}$

Then,

  $\begin{array}{c}V=\frac{1}{3}\pi {\left(3\sqrt{3}\right)}^2\left(6+6\right)\\ =108\pi \\ =339.3\end{array}$