A park is in the form of a square one of whose sides is 100 m . The area of the park excluding the circular lawn in the centre of the park is 8614 m 2. The radius of the circular lawn is?

Q: A park is in the form of a square one of whose sides is 100 m . The area of the park excluding the circular lawn in the centre of the park is 8614 m 2. The radius of the circular lawn is?

Area of park = 100 x 100 = 10000 m2 Area of circular lawn = Area of park - area of park excluding circular lawn = 10000 - 8614 = 1386 Now again area of circular lawn = (22/7) x r2 = 1386 m2 ⇒ r2 = (1386 x 7) / 22 = 63 x 7 = 3 x 3 x 7 x 7 ∴ r = 21 m

21 m
31 m
41 m
None of these

Correct Answer: 21 m

Explanation:

Area of park = 100 x 100 = 10000 m²
Area of circular lawn = Area of park - area of park excluding circular lawn
= 10000 - 8614
= 1386
Now again area of circular lawn = (22/7) x r² = 1386 m²
⇒ r² = (1386 x 7) / 22
= 63 x 7
= 3 x 3 x 7 x 7
∴ r = 21 m

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