LUANDATO wrote:
If the center of a circle lies on a smaller circle, as shown above, what portion of the area of the larger circle is shaded?
A. 5/8
B. 2/3
C. 11/16
D. 3/4
E. 7/9
Let the diameter of the larger circle = 4, implying that the diameter of the smaller circle = 2.
Area of the larger circle = πr² = π(2)² = 4π.
Area of the smaller circle πr² = π(1)² = π.
Area of the unshaded portion = larger circle - smaller circle = 4π - π = 3π.
Thus:
(unshaded portion)/(larger circle) = (3Ï€)/(4Ï€) = 3/4.
The correct answer is
D.
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