A french fry stand at the fair serves their fries in paper cones. The cones have a radius of 222 inches and a height of 666 inches. It is a challenge to fill the narrow cones with their long fries. They want to use new cones that have the same volume as their existing cones but a larger radius of 444 inches. What will the height of the new cones be?

Question

Mathematics

Karina Miranda

21 December, 05:47

A french fry stand at the fair serves their fries in paper cones. The cones have a radius of 222 inches and a height of 666 inches. It is a challenge to fill the narrow cones with their long fries. They want to use new cones that have the same volume as their existing cones but a larger radius of 444 inches. What will the height of the new cones be?

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Answers (1)

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Morgan Wang · Answer 1

The height of the new cone will be calculated as follows:

volume of cone=1/3πr²h

volume of the old cone is:

1/3*π*2²*6

=12 π in³

given that the new cone and old one have the same volume and the new cone has a radius of 4 inches, the the height will be:

12π=1/3*π*4²*h

solving for h we get:

36=16h

thus

h=2.25 inches

thus the height of the new cone is 2.25 inches