SOLUTION: The height of a cylinder is four times its radius. Find a function that models the volume V of the cylinder in terms of its radius r. I know that V=pir^2h, but I don't understand

Algebra ->  Formulas -> SOLUTION: The height of a cylinder is four times its radius. Find a function that models the volume V of the cylinder in terms of its radius r. I know that V=pir^2h, but I don't understand      Log On


   

Question 4265: The height of a cylinder is four times its radius. Find a function that models the volume V of the cylinder in terms of its radius r. I know that V=pir^2h, but I don't understand how to write a function when the height of a cylinder is four times its radius. Thanks
Found 2 solutions by rapaljer, cleomenius:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
V+=+%28pi%29+%28r%5E2%29+%2A+%28h%29 where h = 4r.

Replace the "h" in the formula with "4r".

Now you have V+=+%28pi%29+%28r%5E2%29+%2A+%284r%29 or +V=4%28pi%29+r%5E3


Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
From what I understand in terms of your questions, you are asking to have formula expressed in terms of r.
The formula for the right circular cylinder is V = ( pi * r^2) h
I will adjust this to put h in terms of r:
V = ( pi * r^2 ) 4r
V = 4 *Pi *r^3
This works to V/4 *pi = r^3
In terms of r, we should obtain r = the cubed root of V/ 4 * pi.
To check, I used a radius of 3 in the original formula to obtain the volume or 339.29
Working backwards from the cubed root of V/4 * pi, using 339.29 for V, I obtained a r of 3.
I think the equation you are looking for in this problem is r = cubed root of V / 4 * pi.
Cleomenius.