SOLUTION: A cone and right pyramid have equal height and volumes. If the area of the base of pyramid is 154cm square, find the base radius of the cone

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Question 1210269: A cone and right pyramid have equal height and volumes. If the area of the base of pyramid is 154cm square, find the base radius of the cone
Answer by ikleyn(52864) About Me  (Show Source):
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A cone and right pyramid have equal height and volumes.
If the area of the base of pyramid is 154cm square, find the base radius of the cone
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Let h be the common height.

The volume of the pyramid is  %281%2F3%29%2A154%2Ah.

The volume of the cone is  %281%2F3%29%2Api%2Ar%5E2%2Ah.


Equate the volumes  %281%2F3%29%2A154%2Ah = %281%2F3%29%2Api%2Ar%5E2%2Ah.


Cancel  %281%2F3%29%2Ah  in both sides.  You will get

    pi%2Ar%5E2 = 154

    r%5E2 = 154%2F3.14159265 = 49.02  (rounded)

    r = sqrt%2849.02%29 = 7.001.


ANSWER.  The radius of the cone is about 7 cm.

Solved.