Question

c. 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:

Sharing cone holds 9 times more popcorn than a skinny cone.

Step-by-step explanation:

Height of each cone = 9 inches

Radius of the sharing size cone = 3 times radius of the skinny size cone

Let the radius of skinny size cone = r

Then radius of the sharing size cone = 3r

Volume of the sharing size cone = $\frac{1}{3}(\pi )(\text{Radius})^{2}(\text{Height})$

                                                     = $\frac{1}{3}(\pi )(3r)^{2}(9)$

                                                     = 27πr²

Volume of the skinny size cone = $\frac{1}{3}(\pi )(\text{Radius})^{2}(\text{Height})$

                                                       = $\frac{1}{3}(\pi )(r)^{2}(9)$

                                                       = 3πr²

Ratio of the volumes = $\frac{\text{Volume of sharing size cone}}{\text{Volume of skinny size cone}}$

                                   = $\frac{27\pi r^{2}}{3\pi r^{2} }$

                                   = 9

Therefore, sharing cone holds 9 times more popcorn than a skinny cone.