Question

Someone help please:
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

Answer:

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

Step-by-step explanation:

Cone volume:

$V = \frac{\pi r^{2}h}{3}$

r is the radius and h is the inches.

Skinny-size cone:

Radius is r, height h. So

$V_{sk} = \frac{\pi r^{2}h}{3}$

Sharing size:

Radius is now 3r. So

$V_{sh} = \frac{\pi (3r)^{2}h}{3} = \frac{9\pi r^{2}h}{3} = 3\pi r^{2}h$

How many times more popcorn?

$r = \frac{V_{sh}}{V_{sk}} = \frac{3\pi r^{2}h}{\frac{\pi r^{2}h}{3}} = \frac{3*3\pi r^{2}h}{\pi r^{2}h} = 9$

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