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 =

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

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

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

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