Question : The radii of two concentric circles are $68\;\mathrm{cm}$ and $22\;\mathrm{cm}$. The area of the closed figure bounded by the boundaries of the circles is ______.
Option 1: $4140\pi\;\operatorname{cm^2}$
Option 2: $4110\pi \;\operatorname{cm^2}$
Option 3: $4080\pi\;\operatorname{cm^2}$
Option 4: $4050\pi\;\operatorname{cm^2}$
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Correct Answer: $4140\pi\;\operatorname{cm^2}$
Solution :
The area of a circle with $r$ as the radius $=\pi r^2$
The area of the larger circle $=\pi (68)^2 = 4624\pi \operatorname{cm^2}$
The area of the smaller circle $=\pi (22)^2 = 484\pi \operatorname{cm^2}$
The area of the closed figure $=4624\pi - 484\pi = 4140\pi \operatorname{cm^2}$
Hence, the correct answer is $4140\pi \operatorname{cm^2}$.
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