SOLUTION: Cone and hemisphere volume is same. Find ratio of radius and hight

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Question 818761: Cone and hemisphere volume is same. Find ratio of radius and hight
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
V%5Bc%5D+=+%281%2F3%29pi%2Ar%5E2%2Ah
V%5Bh%5D+=+%281%2F2%29%284%2F3%29pi%2Ar%5E3 (1/2 of the volume of a full sphere)
Simplifying V%5Bh%5D:
V%5Bh%5D+=+%282%2F3%29pi%2Ar%5E3

Since V%5Bc%5D+=+V%5Bh%5D:
%281%2F3%29pi%2Ar%5E2%2Ah+=+%282%2F3%29pi%2Ar%5E3
Now we just solve for r/h:
Dividing both sides by pi:
%281%2F3%29r%5E2%2Ah+=+%282%2F3%29r%5E3
Dividing both sides by r%5E2:
%281%2F3%29%2Ah+=+%282%2F3%29r
Multiplying both sides by 3:
h+=+2r
Divide both sides by 2:
h%2F2+=+r
Divide both sides by h:
1%2F2+=+r%2Fh
So the ratio of the radius to the height is 1/2.