the formula for the area of a circular segment is based on a central angle measured in radians, not in degrees.
area of a circular segment = sector area - triangle area
Problem 1
What is the area of the shaded portion of the circular segment shown in the
figure below, given a = 50 deg and r = 2 ?
Problem 1
Approach:
Look up mensuration formula for a circular segment.
Given:
a = 50 deg
r = 2
By Definition:
Area for circular segment
A =
r^{2}(a - sina)/2
Solve:
A = r^{2}(a - sina)/2
a = 50 deg = 50 deg 2
p rad / 360 deg
a =
0.27778 p rad
r = 2
Substitute:
A =
2^{2}( 0.27778 p - sin 50)/2
A =
0.213
Why did they change 0.2777 and not leave it in degrees
Answer is b) 0.213
a) 0.425
b) 0.213