Question 204152: Find the ratio of the volume of the cone to the volume of the hemisphere if the height of the cone, h, is equal to the diameter of the hemisphere, d.
Thank you for all your help.
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! ASSUME, radius of base of cone is same as radius of hemi sphere
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Given h of cone = dia of hemisphere = 2*r
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Ratio = vol of cone /vol hemisphere
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R = { (1/3)B * h} / { (4/3) pi (r^3)}/2
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R = { (1/3) (pi*r^2) * (2r)} / (4/3) *pi*(r^3)/2
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R = {(2/3)*pi*r^3 }/ ( (4/3) *pi*(r^3)}/2
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R= 2/2 = 1
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Check Let r=2, therefore h=2*2=4
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R={ 1/3 * pi * 2^2 * 4} / {(4/3*pi*8 }/2
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R = 16.755/ 16.755 =1,,,,ok
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note... cone is taller than hemisphere as they overlap
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