Question

A chord in a circle with radius 10 cm subtends an angle of 90° at the center. What is the area of the minor segment?

• A. (25∏-50) sq.cm
• B. (50∏-50) sq.cm
• C. (25∏-100) sq.cm
• D. (100∏-50) sq.cm

Answer 1

Answer:

A. (25∏-50) sq.cm

Given:

• Radius (r=10) cm

• Central angle$(=90^\circ)$

The area of the minor segment is:

$\text{Segment area}=\text{Sector area}-\text{Triangle area}$

1. Area of the sector

$\frac{90}{360}\pi(10)^2=25\pi$

2. Area of the triangle

The two radii form a $(90^\circ)$ angle:

$\text{Triangle area}=\frac12(10)(10)\sin90^\circ=50$

3. Minor segment

$(25\pi-50)$sq.cm