SOLUTION: A circular magnet has an inner radius of r-cm, an outer radius 2cm larger and its depth is the same as the inner radius. If the total volume of the magnet is 120 mulitplied by pi c

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A circular magnet has an inner radius of r-cm, an outer radius 2cm larger and its depth is the same as the inner radius. If the total volume of the magnet is 120 mulitplied by pi c      Log On


   

Question 988251: A circular magnet has an inner radius of r-cm, an outer radius 2cm larger and its depth is the same as the inner radius. If the total volume of the magnet is 120 mulitplied by pi cm^3, find r.
I have written the equation, but cannot solve it.
V= pi x (r+2)^2 x r - pi x r^2 x r
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A circular magnet has an inner radius of r-cm, an outer radius 2cm larger and its depth is the same as the inner radius. If the total volume of the magnet is 120 mulitplied by pi cm^3, find r.
I have written the equation, but cannot solve it.
V= pi x (r+2)^2 x r - pi x r^2 x r
just make equal to 120pi
%28pi%2A%28r%2B2%29%5E2%2Ar%29+-+%28pi%2Ar%5E2%2Ar%29+=+120%2Api
divide thru by pi, multiply r
%28r%28r%2B2%29%5E2%29+-+r%5E3+=+120
FOIL (r+2)(r+2)
r%28r%5E2+%2B+4r+%2B+4%29+-+r%5E3+=+120
r%5E3%2B+4r%5E2+%2B+4r+-+r%5E3+=+120
r^3 cancel so we have
4r%5E2+%2B+4r+=+120
Simplify, divide by 4
r%5E2+%2B+r+=+30
A quadratic equation
r%5E2+%2B+r+-+30+=+0
factors to
(r+6)(r-5) = 0
positive solution
r = 5
:
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