205k views
1 vote
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?

User Equanox
by
8.0k points

1 Answer

5 votes

Answer:

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.

User Mariusz
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories