# 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

May 31, 2018

The cone's volume is 2 times greater.

#### Explanation:

Assuming that by line you meant cone:

The volume of a cone is always $\frac{1}{3}$ 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 $6 \cdot \frac{1}{3}$, or 2 times greater than the cylinder.