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A circular swimming pool is surrounded by a concrete wall 4 feet wide. if the area of the wall is 11/25 of the area of the pool, then the radius of the pool in feet is?

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Let the radius of the pool be r. Then area of the wall and pool = $\pi {(r + 4)^2}$
Area of the pool = $\pi {(r)^2}$
Area of the wall = $\pi {(r + 4)^2} - \pi {(r)^2}$
Given $\pi {(r + 4)^2} - \pi {(r)^2}$ = $\frac{{11}}{{25}}(\pi {r^2})$
${r^2} + 8r + 16 - {r^2} = \displaystyle\frac{{11}}{{25}}{r^2}$
$11{r^2} - 200r - 400 = 0$
Solving r = 20

answered Oct 31, 2013 by Campusgate
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