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 
just make equal to 120pi
{{{(pi*(r+2)^2*r) - (pi*r^2*r) = 120*pi}}}
divide thru by pi, multiply r
{{{(r(r+2)^2) - r^3 = 120}}}
FOIL (r+2)(r+2)
{{{r(r^2 + 4r + 4) - r^3 = 120}}}
{{{r^3+ 4r^2 + 4r - r^3 = 120}}}
r^3 cancel so we have
{{{4r^2 + 4r = 120}}}
Simplify, divide by 4
{{{r^2 + r = 30}}}
A quadratic equation
{{{r^2 + r - 30 = 0}}}
factors to
(r+6)(r-5) = 0
positive solution
r = 5
:
Did this make sense to you?