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    Question

    A circular swimming pool is surrounded by a circular

    path which is 4 m wide. If the area of the path is 44% of the area of the swimming pool, then the radius (in metres) of the pool will be:
    A 16.5 Correct Answer Incorrect Answer
    B 21.5 Correct Answer Incorrect Answer
    C 20 Correct Answer Incorrect Answer
    D 16 Correct Answer Incorrect Answer

    Solution

    Area of a circle = Ο€r2 Let radius of circular pool be β€˜a’ meter Given, Radius of circular path = a + 4 Area of a circular pool = Ο€a2 Area of a pool + circular path = Ο€(a + 4)2 Given, β‡’ Ο€(a + 4)2 – Ο€a2 = 40% Γ— Ο€a2 β‡’ Ο€(a + 4)2 – Ο€a2 = 11/25 Γ— Ο€a2 β‡’ a2 + 8a + 16 – a2 = 11a2 /25 β‡’ 11a2 – 200a – 400 = 0 β‡’ 11a2 – 220a + 20a – 400 = 0 β‡’ 11a(a – 20) + 20(a – 20) = 0 β‡’ a = -20/11 or a = 20 ∴ Radius of a pool is 20 m.

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