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What is a sector ?

A sector is a portion of a circle enclosed by two radii and an arc. Understanding the area of a sector is essential in geometry and real-world scenarios where circular shapes play a role.aces.

Why calculate the sector area ?

Calculating the sector area is vital in various fields such as engineering, physics, and architecture. It provides insights into proportions, helping in design an

Formula

The formula for calculating the area of a sector is straightforward:

$Sector Area = \frac{Central Angle}{360} \times π r^{2}$

where:

π is the mathematical constant (approximately 3.14159)

r is the radius of the circle

Central Angle is the angle subtended by the sector at the center of the circle.

Examples:

Example 1:

Consider a circle with a radius of 8 units and a central angle of 60 degrees.

Using the formula:

$Sector Area = \frac{Central Angle}{360} \times π \times r^{2}$

$Sector Area = \frac{60}{360} \times π \times 8^{2}$

$Sector Area = \frac{1}{6} \times π \times 64$

$Sector Area = 33.5103 units²$

Example 2:

For a circle with a radius of 12 units and a central angle of 120 degrees.

Using the formula:

$Sector Area = \frac{Central Angle}{360} \times π \times r^{2}$

$Sector Area = \frac{120}{360} \times π \times 12^{2}$

$Sector Area = \frac{1}{3} \times π \times 144$

$Sector Area = 150.7964 units²$

Example 3:

Let's explore a scenario where the central angle is the full circle 360 degrees and radius is 10 units.

Using the formula:

$Sector Area = \frac{Central Angle}{360} \times π \times r^{2}$

$Sector Area = π \times 10^{2}$

$Sector Area = \times π \times 100$

$Sector Area = 134.16 units²$

Admission Enquiry

What is a sector ?

Why calculate the sector area ?

Formula

Examples: