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A circular swimming pool is surrounded by a concrete wall 4m wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius (in m) of the pool is :
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- 8
- 16
- 30
- 20
- 8
Correct Option: D
Let the radius of swimming pool be r metre.
Breadth of shaded part = 4 metre
∴ OB = (r + 4) metre According to the question,
π × OB² – π × OA² = π × OA² 25 ⇒ (r + 4)² – r² = r² 25 ⇒ r² + 8r + 16 - r² = r² 25 ⇒ 8r + 16 = r² 25
⇒ 200r + 400 = 11r²
⇒ 11r² – 200r – 400 = 0
⇒ 11r² – 220r + 20r – 400 = 0
⇒ 11r (r – 20) + 20 (r – 20) = 0
⇒ (r – 20) (11r + 20) = 0
⇒ r = 20 metre becauser ≠ - metre 11
