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A cylinder and a cone have the same height, but the base radius of the cylinder is only half that of the cone. If the volume of the cylinder is 1, then what is the volume of the cone?

 Jun 5, 2023
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vol of cyl is H*Pi*r^2

vol of cone is H*Pi*r^2*1/3

 

solve for r in cyl, R=sqrt(1/H*Pi)

since radius of cyl is half that of cone, multiply that by 2 to get radius of cone

cones R= 2*sqrt(1/H*Pi)

put that into cone's formula

r^2 would be 4/H*pi

that times Pi*H would = 4

now times 1/3

cone's vol would be 4/3

 Jun 5, 2023

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