Question

A vendor at a street fair sells popcorn in cones, all of height 9 inches. The

sharing-size cone has 3 times the radius of the skinny-size cone. About how
many times more popcorn does the sharing cone hold than the skinny cone?

Answer 1

The sharing cone holds about 9 times more popcorn than the skinny cone.

Explanation:

The volume of a cone is given by the following formula:

`V = (\pi r^(2)h)/(3)`

In which r is the radius and h is the height.

Two cones:

Both have the same height.

The sharing-size cone has 3 times the radius of the skinny-size cone.

Skinny:

radius r, height h. So

`V_(sk) = (\pi r^(2)h)/(3)`

Sharing size:

radius 3r, height h. So

`V_(sh) = (\pi (3r)^(2)h)/(3) = (9\pi r^(2)h)/(3) = 3\pi r^(2)h`

About how many times more popcorn does the sharing cone hold than the skinny cone?

`r = (V_(sh))/(V_(sk)) = (3\pi r^(2)h)/((\pi r^(2)h)/(3)) = (3*3\pi r^(2)h)/(\pi r^(2)h) = 9`

The sharing cone holds about 9 times more popcorn than the skinny cone.