SOLUTION: I'm not sure how to type out this problem, so I'll do my best. It states to find the polynomial for the shaded area. (Leave results in terms of pie where appropriate. It shows a

Question 125844This question is from textbook Introductory Algebra
: I'm not sure how to type out this problem, so I'll do my best. It states to find the polynomial for the shaded area. (Leave results in terms of pie where appropriate. It shows a circle with the middle cut out. The radius of the entire cirlce is listed as a and the radius from the outside to the inside of the "doughnut" is listed as b. Initially I thought it would be:
pie x a^2 - pie x b^2, but now I'm not sure that that makes sense. Any help on this problem would be greatly appreciated. Thanks! This question is from textbook Introductory Algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find the polynomial for the shaded area. (Leave results in terms of pie where appropriate. It shows a circle with the middle cut out. The radius of the entire circle is listed as a and the radius from the outside to the inside of the "doughnut" is listed as b. Initially I thought it would be:
pie x a^2 - pie x b^2,
--------------------------
Sounds pretty good.
Area of the whole circle, including the hole, is pi(a^2)
Area of the hole is pi(a-b)^2
----------------
EQUATION:
Shaded area = pi(a^2) - pi(a-b)^2
Shaded area = pi[a^2 - (a^2-2ab+b^2)]
Shaded area = pi[2ab-b^2]
======================
Cheers,
Stan H.
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