A circular swimming pool is surrounded by a concrete wall 4 ft. wide. If the area of the concrete wall surrounding the pool is 1125 that of the pool, then the radius of the pool is :

Answer: Option C

Let the radius of the pool be R ft.
Radius of the pool including the wall = (R + 4)ft.
Area of the concrete wall :
$$\begin{array}{rl}& =\pi \left[{\left(R+4\right)}^2-R^2\right]sq.ft\\ & =\pi \left[\left(R+4+R\right)\left(R+4-R\right)\right]sq.ft\\ & =8\pi \left(R+2\right)sq.ft\\ & 8\pi \left(R+2\right)=\frac{11}{25}\pi R^2\\ & \Rightarrow 11R^2=200\left(R+2\right)\\ & \Rightarrow 11R^2-200R-400=0\\ & \Rightarrow 11R^2-220R+20R-400=0\\ & \Rightarrow 11R\left(R-20\right)+20\left(R-20\right)=0\\ & \Rightarrow \left(R-20\right)\left(11R+20\right)=0\\ & \Rightarrow R=20\end{array}$$
∴ Radius of the pool = 20 ft.