A circular swimming pool is surrounded by a concrete wall 4 ft. wide. If the area of the concrete wall surrounding the pool is $$\frac{{11}}{{25}}$$ that of the pool, then the radius of the pool is :
A. 8 ft
B. 16 ft
C. 20 ft
D. 30 ft
Answer: Option C
Solution(By Examveda Team)
Let the radius of the pool be R ft.Radius of the pool including the wall = (R + 4)ft.
Area of the concrete wall :
$$\eqalign{ & = \pi \left[ {{{\left( {R + 4} \right)}^2} - {R^2}} \right]sq.ft \cr & = \pi \left[ {\left( {R + 4 + R} \right)\left( {R + 4 - R} \right)} \right]sq.ft \cr & = 8\pi \left( {R + 2} \right)sq.ft \cr & 8\pi \left( {R + 2} \right) = \frac{{11}}{{25}}\pi {R^2} \cr & \Rightarrow 11{R^2} = 200\left( {R + 2} \right) \cr & \Rightarrow 11{R^2} - 200R - 400 = 0 \cr & \Rightarrow 11{R^2} - 220R + 20R - 400 = 0 \cr & \Rightarrow 11R\left( {R - 20} \right) + 20\left( {R - 20} \right) = 0 \cr & \Rightarrow \left( {R - 20} \right)\left( {11R + 20} \right) = 0 \cr & \Rightarrow R = 20 \cr} $$
∴ Radius of the pool = 20 ft.
Related Questions on Area
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C. 30720 m2
D. 307200 m2
E. None of these
A. 2%
B. 2.02%
C. 4%
D. 4.04%
E. None of these
A. 16 cm
B. 18 cm
C. 24 cm
D. Data inadequate
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The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A. 40%
B. 42%
C. 44%
D. 46%
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