Question

the radius of cylinder is multiplied by 8 while the height is kept the same. What effect does this have on the volume of the cone?

Answer 1

Given:

The radius of a cylinder = r

And the height of the cylinder = h

The radius of the cylinder is multiplied by 8 while the height is kept the same.

We will find the volume of the original and new cylinders

The volume of the original cylinder will be:

$V_1=\pi\cdot r^2\cdot h$

The volume of the new cylinder will be:

$V_2=\pi\cdot(8r)^2\cdot h=64\cdot\pi\cdot r^2\cdot h$

Compare the two volumes:

$\frac{V_2}{V_1}=\frac{64\cdot\pi r^2h}{\pi r^2h}=64$

So, when the radius of the cylinder is multiplied by 8 while the height is kept the volume will be 64 times the original cylinder.