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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 :

sqdancefan

Answer:

  replacement is 1/3 the volume of the original

Step-by-step 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.

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