[tex]\text { The function rule is volume }=\pi \times \text { radius' }^{2} \times(3+4 \times \text { radius) and Volume }=44 \pi \text { when radius }=2[/tex]
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
[tex]\begin{array}{l}{\rightarrow \text { Height }=3 \text { inches }+4 \text { times radius of cylinders base. }} \\\\ {\rightarrow \text { Height }=3+4 \times \text { radius. }}\end{array}[/tex]
Then, [tex]\text { volume }=\pi \times \text { radius' }^{2}\times \text { height } \rightarrow \text { volume }=\pi \times \text { radius }^{2} \times(3+4 \times\text { radius) }[/tex]
So we have written the function rule.
Let us find volume when radius = 2.
[tex]\begin{array}{l}{\text { Then, volume }=\pi \times 2^{2} \times(3+4 \times 2)} \\\\ {\Rightarrow \pi \times 4 \times(3+8)=\pi \times 4 \times 11=44 \pi}\end{array}[/tex]
