Chapter 4.5, Problem 20PPE

To determine

To find: function rule for the volume of the cylinder shown in the question with a height 3 inches more than 4 times the radius of the cylinder’s base. Also, to find volume of the cylinder when it has radius of 2 inches.

Answer to Problem 20PPE

  $V=\pi r^2(3+4r)$ .

Volume of the cylinder when it has radius of 2 inches is equal to $44\pi$ cubic inches

Explanation of Solution

Given information: Height of a cylinder is 3 inches more than 4 times the radius of the cylinder’s base. Volume of the cylinder is $V=\pi r^{2}h$ where $r$ denotes radius and $h$ denotes height of the cylinder.

Calculation:

  

First find the relation between radius $(r)$ and height $(h)$ of the cylinder.

According to the question,

Height of a cylinder is 3 inches more than 4 times the radius of the cylinder’s base.

So,

Height of a cylinder $=$ 3 inches $+$ 4 $\times$ (radius of the cylinder’s base)

  $h=3+4r$ …(i)

Now find the volume of the cylinder using equation (i)

Volume of the cylinder $(V)=\pi r^{2}h$

Put $h=3+4r$

  $V=\pi r^2(3+4r)$

So, the function rule for the volume of the cylinder is $V=\pi r^2(3+4r)$

Now find volume of the cylinder when it has radius of 2 inches.

Put $r=2$ in $V=\pi r^2(3+4r)$

  $\begin{array}{l}$ V=\pi {(2)}^2\left[3+4(2)\right]$=4\pi \left(3+8\right)\\ =4\pi (11)\end{array}$

  $=44\pi$ cubic inches