A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is?
Correct Answer: Option B
let the radius of the pool be Rft
Radius of the pool including the wall = (R+4)ft
Area of the concrete wall = \(\mathrm\pi\left[\left(\mathrm R+4\right)^2-\mathrm R^2\right]\)
= \(\mathrm\pi\left[\left(\mathrm R+4+\mathrm R\right)\left(\mathrm R+4-\mathrm R\right)\right]\;=\;8\mathrm\pi\left(\mathrm R+2\right)\) sq feet
=> 8\(\mathrm\pi\left(\mathrm R+2\right)\;=\;\frac{11}{25}\mathrm{πR}^2\;=>11\mathrm R^{2\;}=200\left(\mathrm R+2\right)\)
Radius of the pool R = 20ft
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