Thread: eplain please? find the area of a Circular sigment

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 =
r²(a - sina)/2


Solve:
A = r²(a - sina)/2
a = 50 deg = 50 deg 2
p rad / 360 deg
a =
0.27778 p rad
r = 2
Substitute:
A =
2²( 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

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