SOLUTION: If the radius of a circle were increased by 2 inches, the area would be increased by 32pi square inches. What is the radius?

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Question 219421: If the radius of a circle were increased by 2 inches, the area would be increased by 32pi square inches. What is the radius?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= original radius
x+2 = new radius

Original area = pi%2Ax%5E2
New area = pi%2A%28x%2B2%29%5E2

The equation is that the NEW area = ORIGINAL area + 32%2Api

pi%2A%28x%2B2%29%5E2+=+pi%2Ax%5E2+%2B32%2Api

Divide both sides by pi

%28pi%2A%28x%2B2%29%5E2%29%2Fpi+=+%28pi%2Ax%5E2%29%2Fpi+%2B%2832%2Api%29%2Fpi
%28x%2B2%29%5E2+=+x%5E2+%2B+32


x%5E2+%2B+4x+%2B4=+x%5E2%2B32

Subtract x^2 from each side:
4x%2B4=32
4x=28
x=7 inches

Check: Original area = pi%2A7%5E2=49%2Api
New area = pi%2A9%5E2=+81%2Api

Indeed, the area IS increased by 32%2Api sq inches.

R^2

Dr. Robert J. Rapalje