SOLUTION: 18. Solve for the indicated letter. Solve the formula S = 1/3 πr2h + 4πrh for r.

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Question 315592: 18. Solve for the indicated letter.
Solve the formula
S = 1/3 πr2h + 4πrh for r.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
18.Solve for the indicated letter.
Solve the formula.
S = 1%2F3pi%2Ar%5E2h+%2B+4pi%2Arh for r.
:
1%2F3%28pi%2Ar%5E2h%29+%2B+%284pi%2Arh%29 = S
Multiply by 3
%28pi%2Ar%5E2h%29+%2B+3%284pi%2Arh%29 = 3S
:
%28pi%2Ar%5E2h%29+%2B+%2812pi%2Arh%29 = 3S
Factor out pi*h
pi*h(r^2 + 12r) = 3S
:
divide both sides by pi%2Ah%29
r^2 + 12r = %283S%29%2F%28pi%2Ah%29
:
Arrange as a quadratic equation
r^2 + 12r - (%283S%29%2F%28pi%2Ah%29) = 0
:
Solve for r using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
In this equation: x = r a=1; b=12; c=-%283S%29%2F%28pi%2Ah%29
r+=+%28-12+%2B-+sqrt%2812%5E2-4%2A1%2A%28%28-3S%29%2F%28pi%2Ah%29%29+%29%29%2F%282%2A1%29+
:
r+=+%28-12+%2B-+sqrt%28144-4%28%28-3S%29%2F%28pi%2Ah%29%29+%29%29%2F2+
:
r+=+%28-12+%2B+sqrt%28144%2B%28%2812S%29%2F%28pi%2Ah%29%29+%29%29%2F2+; I think only the positive solution is wanted here