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What will be the area of the shaded region, if in the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle, with OA=20cm?

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228 cm 2

230 cm 2

226 cm 2

234 cm 2

answer is A.

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Detailed Solution

We have to find the area of the shaded region, if in the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle, with OA=20cm.
Question Image

In the right triangle AOB,
By Pythagoras’ Theorem

O B 2 = O A 2 + A B 2 = 202 + 202 = 400 + 400 = 800 ∴ O B 2 = 800

Calculating the area of the shaded region,
Area of a quadrant of a circle

= 14 π (r) 2

, where r is the radius.
Area of the shaded region = Area of quadrant OPBQ − Area of Square OABC

= 14 π (O B) 2 − (O A) 2 = 14 × 3.14 × 800 − 400 = 628 − 400 = 228 cm 2

So, the area of the shaded region is

228 cm 2 .

Therefore, option 1 is correct.

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