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:Solution
Area of a circle = Οr2 Let radius of circular pool be βaβ meter Given, Radius of circular path = a + 4 Area of a circular pool = Οa2 Area of a pool + circular path = Ο(a + 4)2 Given, β Ο(a + 4)2 β Οa2 = 40% Γ Οa2 β Ο(a + 4)2 β Οa2 = 11/25 Γ Οa2 β a2 + 8a + 16 β a2 = 11a2 /25 β 11a2 β 200a β 400 = 0 β 11a2 β 220a + 20a β 400 = 0 β 11a(a β 20) + 20(a β 20) = 0 β a = -20/11 or a = 20 β΄ Radius of a pool is 20 m.
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