SOLUTION: The volume V of a cylindrical can is v=(pi)r^2h, where r is the radius of the base, and h is the heighth of the cylinder. if the radius of the cylinder is decreased by 25%, by how

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Question 718514: The volume V of a cylindrical can is v=(pi)r^2h, where r is the radius of the base, and h is the heighth of the cylinder. if the radius of the cylinder is decreased by 25%, by how many % should its heighth icrease, so that the cylinder has the same volume v? round your answer to the nearest 10th of a %.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the initial height, h and the increased height, H. We want initial and increased volumes to be the same.
I am using normal fraction form in the steps. 25% decrease means 1/4 decrease, meaning 3/4 of original value for r.
V=pi%2Ar%5E2%2Ah=pi%28%283%2F4%29r%29%5E2%2AH
pi%2Ar%5E2%2Ah=pi%2Ar%5E2%283%2F4%29%5E2%2AH
h=%283%2F4%29%5E2%2AH, divided by sides by pi%2Ar%5E2
h%2F%28%283%2F4%29%5E2%29=H, divided both sides by %283%2F4%29%5E2
1%2F%28%283%2F4%29%5E2%29=H%2Fh, divided both sides by h.
highlight%28H%2Fh=16%2F9%29, we want this ratio because this is how many times h must be increased to become H, to keep V the same. You can convert into its percent increase if desired.