Question 1186076: The volume of water Vm^3, is directly proportional to the square of its cross-sectional radius, R m. If the radius of the pipe is increased by 150%, find the percentage increase of the volume.
Found 4 solutions by Alan3354, josgarithmetic, greenestamps, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The volume of water Vm^3, is directly proportional to the square of its cross-sectional radius, R m. If the radius of the pipe is increased by 150%, find the percentage increase of the volume.
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"increased by 150%" ---> 100% + 150% = 250%
r is multiplied by 2.5
V is multiplied by 2.5^2 = 6.25
An increase of 5.25 or 525%
Answer by josgarithmetic(39617)  (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The problem says the volume of water (in the pipe), V, is proportional to the square of the cross-sectional radius, r. That means we are talking about a pipe of fixed length. So when the radius is increased, the length remains the same.
If the radius r of the pipe is INCREASED BY 150%, then the new radius is r plus 150% of r, which is 2.5r.
Then, since the volume is proportional to the square of the radius, the volume is increased by a factor of (2.5)^2 = 6.25.
And that means the percent INCREASE in the volume is 525%.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
The volume of water Vm^3  , is directly proportional to the square
of its cross-sectional radius, R m. If the radius of the pipe is increased by 150%, find the percentage increase of the volume.
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The solution by @josgarithmetic is totally wrong, as usual for most his solutions.
Ignore it, for your safety.
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