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^2πr2

Area of wall = \pi (r+4)^2-\pi r^2π(r+4)2−πr2

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^2π(r+4)2−πr2=2511πr2

\pi ((r+4)^2-r^2)=\frac{11}{25} \pi r^2π((r+4)2−r2)=2511πr2

((r+4)^2-r^2)=\frac{11}{25} r^2((r+4)2−r2)=2511r2

(r+4)^2=\frac{11}{25} r^2+r^2(r+4)2=2511r2+r2

(r+4)^2-\frac{36}{25} r^2=0(r+4)2−2536r2=0

Solving

r = 20

Hence the radius of the pool is 20 feet.