I have some math questions, will somebody please help me with them?

Question

1. A 20° sector in a circle has an area of 21.5π yd². What is the area of the circle?

(I think the answer is 1215.18 but I am not sure.)

2. What is the area of a sector with a central angle of 2π/9 radians and a radius of 16.7 ft? (Round to nearest hundredth.)

3. What is the area of a sector with a central angle of 2π/9 radians and a diameter of 20.6 mm? (Round to nearest hundredth.)

Answer 1

1. 20 degrees is 20/360 of a complete circle.

 

Hence if the whole circle has an area of A

 

then 20/360 * A = 21.5*π

 

therefore A = 360/20*21.5π = 18*21.5*3.142 = 1216 sqr. yds

 

2. 2π/9 is 2π/9/2π = 1/9 the of the entire circle (remember that the circle is 2π radians.

 

Hence area of sector = 1/9 * π * (16.7)²  = 97.3 sqr. ft.

 

3. Similarly area of sector = 1/9 * π * (10.3)^{2  =} 37.04 sqr. mm