Find the radius of a minor sector of a circle with perimeter 14cm and area 10cm^2.

Question

Find the radius of a minor sector of a circle with perimeter 14cm and area 10cm^2.
Then find the radius of a major sector of a circle with perimeter 14cm and area 10cm^2.

Answer 1

 

 Area = 10 = X/360 * pi * radius^2 <--- equation I

 

 

Perimeter = 14 = X/360 * pi * 2 * radius

 

14*360/2 = pi*X*radius

 

2520 = pi*X*radius <---- equation #2

 

 

 

 

10 =X/360*pi*radius^2

 

3600 = X*pi*radius*radius

 

3600 = 2520 * radius

 

360 = 252 * radius

 

180 = 126 * radius

 

90 = 63 * radius

 

10 = 7 * radius

 

radius = 10/7