Question

pete runs an ice cream stand that also sells snow cones served in paper cones. the paper cones he usually uses have a diameter of 6 inches and a height of 2 inches, but his supplier is out of them. as a replacement, he purchases paper cones with a diameter of 2 inches and a height of 6 inches. how do the volumes of the original and replacement cones compare?

Answer 1

replacement is 1/3 the volume of the original

Explanation:

You want to compare the volumes of a cone with diameter 6 in and height 2 in to one with a diameter of 2 in and height of 6 in.

Volume

The volume of a cone is jointly proportional to the height and the square of the diameter:

V ∝ d²h

Ratio

The ratio of the volume of the replacement cone to the original is ...

r = V2/V1 = ((2 in)²(6 in))/((6 in²)(2 in) = 2/6 = 1/3

The replacement cone has 1/3 the volume of the original.