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In the given figure, two concentric circles with center O have radii 21cm and 42cm , If ∠AOB=60∘ , find the area of the shaded region.

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3652 cm2

3456 cm2

3564 cm2

3256 cm2

answer is B.

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Detailed Solution

As the angle of the minor sector for both the bigger and smaller circles is = 60∘.
So, the angle of the major sector for both the bigger and smaller circles = 300∘.
The formula for the area of the sector of circle is equal to

\frac{θ}{360} π r^{2}

The radius of the bigger circle = 42cm
The area of the major sector of bigger circle is:
A=

\frac{θ}{360} π r^{2}

= \frac{300}{360} \times 3.14 \times {(42 cm)}^{2}

= \frac{5}{6} \times 3.14 \times 1764

= 4620 c m^{2}

The radius of the smaller circle = 21cm
angle for the major sector of this circle= 300∘ .
The area of the major sector of smaller circle is:
A=

\frac{θ}{360} π r^{2}

= \frac{300}{360} \times 3.14 \times {(21 cm)}^{2}

= \frac{5}{6} \times 3.14 \times 441

= 1155 c m^{2}

So, the area of the shaded region is equal to

4620 c m^{2} - 1155 c m^{2} = 3465 c m^{2}

.
Therefore, the area of the shaded region is equal to 3465cm2.
So, the correct answer is “ 3465cm2”.

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