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Nookie1986 [14]
3 years ago
15

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

Mathematics
1 answer:
Tatiana [17]3 years ago
3 0

Answer:

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

Step-by-step explanation:

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

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

Sharing size:

radius 3r, height h. So

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

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