find the area of a circle of radius 35 cm.if a sector of angle 80° is removed from the circle, what area is left

Question

area of plane shapes

Answer 1

find the area of a circle of radius 35 cm.if a sector of angle 80° is removed from the circle, what area is left

Area of sector, A1 = (1/2).r^2.theta, where theta = 80 degrees = (80/180)*pi radians, giving A1 = pi.r^2(2/9)

Area of circle, A2 = (1/2).r^2.theta, where theta = 2pi, giving A2 = pi.r^2

Area left, A3 = A2 - A1 = pi.r^2 - (2/9)pi.r^2 = (7/9)pi.r^2

Using r = 35 cm,

A3 = (7/9)pi*1225

A3 = 952.78.pi cm^2 = 2,993.24 cm^2  Area of circle = A2 = 1225.pi cm^2 = 3,848.45 cm^2

Answer 2

Area of circle  =  pi * r^2 = 35^2 * pi = 1225pi cm^2 = 3848.45 cm^2 (pi = 3.14159)

left area = 280 * (3848.45 / 360) = 2993.24 cm*2  (280 degrees = 360 - 80)

Area of circle = 3848.45 cm^2

Left area after removing the 80 degrees sector = 2993.24 cm^2