Question

A french fry stand at the fair serves their fries in paper cones. The cones have a radius of 2 inches and a height of 6 inches. It is a challenge to fill the narrow cones with their long fries. They want to use new cones that have the same volume as their existing cones but a larger radius of 4 inches.
What will the height of the new cones be?

Answer 1

The formula for the volume of a right circular cone is V = $\pi r^{2} h$. In solving for the volume of the first french fries cones V = $\pi ( 2^{2} )(6)$ = 75.398 $in^{3}$. In solving for the height of the second french fries cones with a new radius of 4, the formula is rearranged to h =$\frac{V}{ \pi r^{2} }$ = $\frac{75.398}{ \pi (4^{2}) }$ = 1.5 in or inches. The height of the new cones will be 1.5 inches.