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A circular pool of radius 10 m is built inside a circular garden of radius 24 m. To compensate the area lost due to the construction of the pool, the radius of the garden is extended by ‘r’ m, as a result of which, the garden is still circular and the area of the garden excluding the area of the pool remains the same. Find the value of r (in m).

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3 m

4 m

2 m

1 m

answer is B.

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Detailed Solution

The area of the garden = π × (24)² = 576 π

The area of the pool = π × (10)² = 100 π

∴π × (24 + r)² − π × (24)² = 100 π

⇒ (24)² + r² + 48 r − (24)² = 100

⇒ r² + 48r − 100 = 0

⇒ r² + 50r − 2r − 100 = 0

⇒ r (r + 50) − 2 (r + 50) = 0

⇒ r = 2 m

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