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

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

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 =
`(1)/(3)(\pi )(\text{Radius})^(2)(\text{Height})`

=
`(1)/(3)(\pi )(3r)^(2)(9)`

= 27πr²

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

=
`(1)/(3)(\pi )(r)^(2)(9)`

= 3πr²

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

=
`(27\pi r^(2))/(3\pi r^(2) )`

= 9

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