A geometry problem by Sagar Bagchi

Geometry Level 1

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

2.44 7 1.132 1 1.732

Sagar Bagchi by Sagar Bagchi , 28, India

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1 solution

Original area of the garden: 1 2 2 × π = 144 π 12^{2}\times\pi=144\pi sq. m

Area of the pool: 5 2 × π = 25 π 5^{2}\times\pi=25\pi sq. m

Area of the extended garden (incl. pool): 25 π + 144 π = 169 π 25\pi+144\pi=169\pi sq.m

And 169 = 1 3 2 169=13^{2} , so r = 13 − 12 = 1 \boxed{r=13-12=1} .

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