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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?

Respuesta :

CastleRook
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

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