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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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  1. 21 December, 07:54
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    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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