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What is the area of the circular ring included between two concentric circles of radius $14$ cm and $10.5$ cm ?

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269 c m^{2}

324 c m^{2}

255 c m^{2}

148 c m^{2}

answer is D.

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Detailed Solution

It is given to find the area of the circular ring included between two concentric circles.
A draft picture has been drawn below.
Question Image

Let R be the radius of the larger circle.
Hence

R = 14 cm

Let

r

be the radius of the smaller circle.
Hence

r = 10.5 cm

Area of the circular ring

=

area of the larger circle - area of the smaller circle

\Rightarrow π R^{2} - π r^{2}

\Rightarrow \frac{22}{7} \times (R^{2} - r^{2})

\Rightarrow \frac{22}{7} \times (14^{2} - {10.5}^{2})

\Rightarrow 269.5 {cm}^{2}

\approx 269 {cm}^{2}

Hence, required solution is 269 sq. cm
Hence, option 4 is correct.

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