Question

write a function rule for the volume of the cylinder with a hight 3 inches more than 4 times the radius of the cylinders base. what is the volume of the cylinder when it has a radius of 2 inches?​

Answer 1

`\text { The function rule is volume }=\pi * \text { radius' }^(2) *(3+4 * \text { radius) and Volume }=44 \pi \text { when radius }=2`

SOLUTION:

Given that, we have to write a function rule for the volume of the cylinder with a height 3 inches more than 4 times the radius of the cylinders base. And the volume of the cylinder when it has a radius of 2 inches

Now, let us write the function rule.

We are given that, height 3 inches more than 4 times the radius of the cylinders base

`\begin{array}{l}{\rightarrow \text { Height }=3 \text { inches }+4 \text { times radius of cylinders base. }} \\\\ {\rightarrow \text { Height }=3+4 * \text { radius. }}\end{array}`

Then,
`\text { volume }=\pi * \text { radius' }^(2)* \text { height } \rightarrow \text { volume }=\pi * \text { radius }^(2) *(3+4 *\text { radius) }`

So we have written the function rule.

Let us find volume when radius = 2.

`\begin{array}{l}{\text { Then, volume }=\pi * 2^(2) *(3+4 * 2)} \\\\ {\Rightarrow \pi * 4 *(3+8)=\pi * 4 * 11=44 \pi}\end{array}`