A man builds a circular pool of radius 5 m inside a circular garden of radius 12 m. In order to comp

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31 Jul 2015 Area

A man builds a circular pool of radius 5 m inside a circular garden of radius 12 m. In order to compensate the area lost due to the construction of pool, he extends the radius by 'r' m while keeping the garden still circular, so that the area of the garden remains the same. The value of r (in m) is

OPtion

1) 1
2) 3
3) Sqrt(3)
4) Sqrt(5)
5) 6-Pi
6) Sqrt(12-5)
7) 5/Pi
8) Sqrt(7)
9) Sqrt(5)-Pi
10)None of these

Solution

Area of garden = Pi*12^2 = 144 Pi m^2
Area of pool = Pi*(5)^2 = 25 Pi m^2
Therefore Pi*(12+r)^2 - Pi*(12)^2 = 25 Pi m^2
Or r^2 + 24 r - 25 = 0
(r+25) (r-1) = 0
r = 1
Option 1)

Correct Option: 1 Best Solution (1)