Area of Circles

Question

A circle has a radius of 8 ft. What is the area of the sector formed by a central angle measuring 5(3.14)/4 radians?

Answer 1

Method 1

 

Area of full circle pi*r²   (pi = 3.14)

 

the central angle, 5*pi/4 is a sector of the circle, with 2*pi the central angle of the full circle

 

therefore fraction of full circle =  (5*pi/4)/2*pi = 5/8

 

Therefore area of sector = 5/8 * pi * 8²  = 125.6 ft²

 

 

Method 2

 

Area of scetor = 1/2* r² * theta  (theta = angle subtended bat center of circle by sector)

 

= 1/2 * 8² * 5 * pi /4 = 125.6 ft²

 

 

Answer 2

Hi Laura

Area of the full circle = pi R² =3.14 * 8*8 ft²

New angle = 5 pi / 4 radian 

which is 5/8 times the area of full circle  (as angle of full circle = 2*3.14 radian )

Area of sector = 5/8 * (pi R² )=125.6 ft ^2