SOLUTION: I have been given the volume of a cone, 100 in cubed. I need to find the function that models the height of the cone in terms of it's radius. Any help would be appreciated.

Algebra ->  Formulas -> SOLUTION: I have been given the volume of a cone, 100 in cubed. I need to find the function that models the height of the cone in terms of it's radius. Any help would be appreciated.      Log On


   

Question 5052: I have been given the volume of a cone, 100 in cubed. I need to find the function that models the height of the cone in terms of it's radius. Any help would be appreciated.
Found 3 solutions by rapaljer, cleomenius, Alan3354:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This is the formula for the volume of a cone:
V=+%281%2F3%29+%2A+pi+%2A+r%5E2+%2A+h+

You are given the volume V = 100, so substitute that for V in the formula:
100+=+%281%2F3%29+%2A+pi+%2A+r%5E2+%2A+h+

Next, multiply both sides of the equation by 3, so as to eliminate the fraction:
3%2A+100+=+3%2A+%281%2F3%29+%2A+pi+%2A+r%5E2+%2A+h+
300+=+pi+%2A+r%5E2+%2A+h+

Now, you need to get h by itself, so divide both sides by +pi+%2A+r%5E2
300+%2F%28+pi+%2A+r%5E2%29+=+%28pi+%2A+r%5E2+%2A+h%29%2F+%28pi+%2A+r%5E2%29+
300+%2F%28+pi+%2A+r%5E2+%29+=+h+

R^2 at SCC








Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
I am not sure I understand your question.
The way it is phrased, we have two unknowns, the radius and the height.
THe previous answer will give you the height as determined by a known radius, if this is what you are looking for.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
V+=+pi%2Ar%5E2%2Ah%2F3+=+100
pi%2Ar%5E2%2Ah%2F3+=+100
pi%2Ar%5E2%2Ah+=+300
r%5E2%2Ah+=+300%2Fpi
h+=+300%2F%28pi%2Ar%5E2%29
-------------------------
PS it's = it is