Question

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

Answer 1

Answer:

The radius of the pool is 20 feet.

Step-by-step explanation:

Let the radius of the pool be r

A circular swimming pool is surrounded by a concrete wall 4 ft wide.

Outer radius = r+4

Area of Pool = $\pi r^2$

Area of wall = $\pi (r+4)^2-\pi r^2$

Since we are given that the area of the wall is 11/25 of the area of the pool

So, $\pi (r+4)^2-\pi r^2=\frac{11}{25} \pi r^2$

$\pi ((r+4)^2-r^2)=\frac{11}{25} \pi r^2$

$((r+4)^2-r^2)=\frac{11}{25} r^2$

$(r+4)^2=\frac{11}{25} r^2+r^2$

$(r+4)^2-\frac{36}{25} r^2=0$

Solving

r = 20

Hence the radius of the pool is 20 feet.