Multiple choice

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

  1. $1$
  2. $\displaystyle \sqrt{5}$
  3. $\displaystyle \sqrt{7}$
  4. $\displaystyle \frac{5}{\pi }$
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A Correct answer
AI explanation

Assuming the stated dimensions of 5 m and 12 m represent the respective radii of the pool and the garden, the area lost to the pool is pi * 5^2 = 25*pi. To compensate, the total garden area pi * 12^2 = 144*pi is extended by a factor of r, establishing the equation pi*(12 + r)^2 = 169*pi. Taking the square root of both sides results in 12 + r = 13, which means r equals 1.

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