Chapter 1.1, Problem 35PPS

To determine

To write: an expression to represent the volume of the given cone.

Answer to Problem 35PPS

  $V=6\pi x^3$

Explanation of Solution

Given information:

A cone is given as shown:

  

Volume of a cone is

  $V=\frac{1}{3}\pi r^{2}h$

Where r is radius of the cone and h is the height.

Calculation:

Consider the given cone.

  

Here, radius is $3x$ and height is $2x$ .

So, expression for volume of the cone can be evaluated as

  $\begin{array}{c}V=\frac{1}{3}\pi r^{2}h\\ =\frac{1}{3}\pi {\left(3x\right)}^2\left(2x\right)\\ =\frac{1}{3}\pi \left(9x^2\right)\left(2x\right)\\ =3\pi x^2\cdot 2x\\ =6\pi x^3\end{array}$

Hence, the expression for volumeis $6\pi x^3$ .