Areas Between Curves: Quiz


Problem 4

Find the area of the face (not including the mouth and eyes) in the drawing below.

The large circle has radius 3 and is centered at the point (0, 2). The mouth is the area bounded by the curves
y = x2 and y = 0.5x2 + 0.5. The eyes are circles of radius 0.5 centered at the points (–1, 2.5) and (1, 2.5).


Answers, problem 4

The area of the large circle is π(3)2, the area of each small circle is π(1/2)2. The area of the mouth is

The net area of the face is 9π – 2/3π – 2/3.


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