Answer:
Answer: 56*pi
Step-by-step explanation:
The easiest way is to find the area of the circle and subtract the area of the sector.
Area of the circle
d = 16 cm given
d = 2*r definition
16 = 2*r divide by 2
16/2 = 2r/2
r = 8
Area of the circle = pi * r^2
Area of the circle = pi * 8^2
Area of the circle = 64 pi
Area of the sector
Area of sector = (theta/360) * pi * r^2
Area of sector = 45/360 * pi * 64
Area of sector = 1/8 * pi * 64
Area of sector = 8 * pi
Area of the shaded area
Area of the shaded area = 64 * pi - 8*pi = 56*pi
Note: There is a shorter way, but one can never be confident of getting an angle greater than 180 correct.
360 - 45 = 315
Area of the sector = 315/360 * pi * r2
Area of the sector = 7/8 * pi * 64
Area of the sector = 7 * pi * 8
Area of the sector = 56*pi
