If the radius of a cylinder increases by a factor of 8, by what factor does the volume increase

Factor of 64.

Step-by-step explanation:

Volume of cylinder: V = πr²h, where V is the volume, r is the radius and h is the length or height.

Now supposing that we multiply the radius by 8. How does the cylinder volume compare to the original volume?

Original volume: V = πr²h

New volume: V = π (8r) ²h = 64πr²h

So the volume increases by a factor of 64.