A cone and a pyramid have the same height and same volume. If the radius of the base of the cone is r, what is the side length of the square base of the pyramid?

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nsolorzano61181 nsolorzano61181

02-05-2018
Mathematics

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A cone and a pyramid have the same height and same volume. If the radius of the base of the cone is r, what is the side length of the square base of the pyramid?

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popalabdulqayou popalabdulqayou · Answer 1 · 2018-05-05T23:01:01+02:00

popalabdulqayou popalabdulqayou

05-05-2018

let Vc : cone's volume, Vp : pyramid's Volume, r radius, h height. w width and l length.

Vc=πr²h/3

Vp=(lwh)/3

make it equal to each other and cancel out the 3.

πr²h = lwh

heights will cancel out

πr²=lw

l=(πr²)/w

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