Problem 253

Problem  253

Garden Area Problem. A designer created a garden from two concentric circles whose equations are as follows: (x + 2)² + (y – 6)² = 16 and (x + 2)² + (y – 6)² = 81

The area between the circles will be covered with grass. What is the area of that section?

 

Solution

 

First circle equation is

(x + 2)² + (y – 6)² =16………..(1)

Radius( r ) of this given  circle is √16=4

And area of this circle = A=πr^2

A = π4²

A = 3.14×16

A=50.24 sq.units

Second circle’s equation

(x + 2²) + (y – 6)² = 81………..(2)

Radius( r ) of this given  circle is √81=9

And area of this circle = A= πr ²

A=π9 ²

A=3.14×81

A=254.34 sq.units

So difference between two area of two circles

=254.34 – 50.24

=204.1 sq units