Question 974323: What happens to the volume of a cylindrical tank if its radius is doubled?
Answer by Okamiden(22)   (Show Source):
You can put this solution on YOUR website! First, we need the equation for volume of a cylindrical tank. It's Pi*r^2*h
In other words, it's Pi times Radius Squared times Height.
Example : if the radius is 3 meters and the height is 1 meter, we get this answer:
Pi * (3^2) * 1 = 9 Pi square meters.
Now, what happens if we took a radius of 6 meters instead, which is double the radius?
Pi * 6^2 * 1 = 36 Pi square meters. Notice we went from 9 Pi to 36 pi when we doubled the radius, and 36 Pi is 4 times as big as 9 Pi.
Thus, we can imagine that when you double the radius, you get a volume 4 times as big. We found this with an example, but it's possible your teacher would prefer you use algebra to find it. If yes, read below :
Formula Pi * r^2 * h.
Radius of the cylindrical tank is an unknown number, let's call it k.
So, r = k. Volume of the original tank is Pi * k ^2 * h.
What happens if we take a radius twice as big? instead of r = k in the formula, we'd have r = 2k. Using the formula, we get this :
Pi * (2k)^2 * h
Distributing the exponent : Pi * 4 * k^2 * h
Or : 4 * Pi * k^2 * h
This is 4 times the volume of the original cylindrical tank of radius k.
Hope that wasn't too confusing!
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