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What is the area of a semicircle with a diameter of $16$ inches?

  1. $32 \pi$ square inches
  2. $64 \pi$ square inches
  3. $128 \pi$ square inches
  4. $256 \pi$ square inches
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Area of circle =  $\pi\times r^{2}=\pi \times \frac{d^{2}}{4}=\pi\times \frac{256}{4}=64\pi$ square inches

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Area of semicircle = $\frac{1}{2} \times $ area of circle $= \frac{\pi r^2}{2} $

Diameter $=16$ inches $\implies $ radius $=8$ inches

Required Area $=\frac{\pi r^2}{2} = \frac{\pi \times 8^2}{2} = 32\pi $ square inches.

Option (A) is correct.

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