SOLUTION: find the volume of the largest cylinder with a circular base that can be inscribed in a cube which has a volume of 27m^3.

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Question 610699: find the volume of the largest cylinder with a circular base that can be inscribed in a cube which has a volume of 27m^3.

Found 2 solutions by lwsshak3, jamesgunasekaran:
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
find the volume of the largest cylinder with a circular base that can be inscribed in a cube which has a volume of 27m^3.
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let x=length= width= height of cube
volume=x^3=27m^3
x=3 m
..
length of cylinder=3 m
Diameter of circular base=3 m
volume of cylinder=πr^2*3=π(3/2)^2*3=27π/4
ans:
largest cylinder with a circular base that can be inscribed in the cube=27π/4 m^3

Answer by jamesgunasekaran(1) (Show Source):
You can put this solution on YOUR website!
The volume of a cube with side s is . Hence find the side of the cube
which is going to be .
Hence a largest cylinder with base inscribed inside a cube will have the diameter 3 meters. and its maximum height will be the height of the cube. Hence in this case it is 3 meters. Hence the volume of a cylinder with the above parameters will be
Hence volume is = =