# eplain please? find the area of a Circular sigment

• Jun 7th 2012, 05:01 PM
zbest1966
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
a =
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

a) 0.425
b) 0.213
• Jun 8th 2012, 04:40 AM
skeeter
Re: eplain please? find the area of a Circular sigment
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

$\displaystyle A = \frac{\theta}{2\pi} \cdot \pi r^2 - \frac{1}{2} r^2 \sin{\theta}$

$\displaystyle A = \frac{r^2}{2} \left(\theta - \sin{\theta}\right)$