SOLUTION: Beginning at the origin, a spiral is constructed from 3 semi circles with centres at (1,0),(0,0),(2,0). The area of the shaded region, in u^2 is: A) 7 π-2 √3/6 B) 8 π-√3/

Question 1167553: Beginning at the origin, a spiral is constructed from 3 semi circles with centres at (1,0),(0,0),(2,0). The area of the shaded region, in u^2 is:
A) 7 π-2 √3/6
B) 8 π-√3/3
C)8 π-6 √3/3
D) 3 π -2 √3
E) 11 π -6√3/3

https://imageshack.com/i/pmBbsOMDj
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Call the origin O. Let A(2,0) be the center of the third semicircle, and let B(0,b) be the y-intercept of that third semicircle.

Triangle AOB is a 30-60-90 right triangle, because OA=2 and AB=4. That makes OB .

The shaded region is (a) one-half the area of the second semicircle with radius 2, plus (b) one-third the area of the third semicircle (because angle BAO is 60 degrees), minus (c) the area of triangle AOB.

(a)
(b)
(c)

ANSWER:

Note answer choices A, B, C, and E are all shown incorrectly, because required parentheses are missing.

Answer choice E is supposed to be the right answer:

But answer choice E as shown, , is incorrect.

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