Chapter 7, Problem 17SGR

To determine

To Find: The volume of the given cylinder.

Answer to Problem 17SGR

  $V=45\pi x^3\text{ cubic unit}$

Explanation of Solution

Given information:

The cylinder with radius $r=3x$ and height $h=5x^2$ and volume of cylinder is $V=\pi r^{2}h$

Concept and Formula Used:

Rule of exponent.

  $a^n\times a^n=a^{m+n},{\left(a^n\right)}^m=a^{m\times n}$

Calculation:

The given cylinder

Where radius $r=3x$ and height $h=5x^2$ and volume of cylinder is $V=\pi r^{2}h$

Putting the value of radius and height in the volume

  $\begin{array}{l}V=\pi {\left(3x\right)}^2\left(5x\right)\\ \text{Using}{\left(a^n\right)}^m=a^{m\times n}\\ V=\pi \left(3^2{x}^2\right)\left(5x\right)\\ V=\pi \left(9x^2\right)\left(5x\right)\\ \text{Arranging the like terms}\\ V=\pi \left(9\times 5x^2\times x\right)\\ V=45\pi x^3\text{ cubic unit}\end{array}$

Conclusion:

  $V=45\pi x^3\text{ cubic unit}$