Question

A cone and a cylinder have the same area base. The line's height is 6 times the height of the cylinder. How much greater is the volume of the cone? My teacher says you have to show your work

Answer 1

The cone's volume is 2 times greater.

Explanation:

Assuming that by line you meant cone:

The volume of a cone is always `1/3` the volume of a cylinder, provided the bases and height are the same.

This is visible from the formulas for each solid.

`V_(con"e) = 1/3cancel(pir^2h)`

`V_(cyli"nder) = cancel(pir^2h)`

So if the height of the cone is 6 times larger than that of the cone, then the volume is `6 * 1/3`, or 2 times greater than the cylinder.