A) \[4\pi +8\]
B) \[8\pi +4\]
C) \[8\pi +8\]
D) \[16\pi +4\]
Correct Answer: A
Solution :
Here, as we can see from the figure that the shaded region is a semicircle. Perimeter of the shaded region is sum of the length of the diameter AB and the circumference of a semicircle P. Now by distance rule, \[AB=\sqrt{{{(7-(1))}^{2}}+{{(0-0)}^{2}}}=\sqrt{{{(8)}^{2}}}=8.\] So, diameter of circle P, \[D=8\] \[\therefore \] Circumference of semicircle \[P=\frac{1}{2}(\pi \,D)=\frac{1}{2}\,(\pi (8))=4\pi \] So, perimeter of shaded region \[=4\pi +8\]
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