Area of a Quarter Circle Formula

Formula for the area of a quarter circle with radius r is:

A = (πr²) / 4

Derivation of the Formula

Area of a Circle: The formula for the area of a circle with radius r is given by, πr².

Quarter of a Circle: Since a quarter circle is one-fourth of a full circle, the area of a quarter circle will be one-fourth of the area of a full circle.

Area of Quarter Circle = (1/4) × Area of Circle

Thus, Area of quarter = (πr²) / 4.

So, the formula for the area of a quarter circle with radius r is: (πr²) / 4.

Calculating the Area of a Quarter Circle

We can use the formula discussed above i.e., Area of Quarter Circle = (πr²) / 4

Let’s consider an example for better understanding.

Example: Find the area of Quarter Circle with radius 6 units.

Solution:

Given: radius = 6 units

Area of Quarter Circle = (πr²) / 4

Thus, Area = (π × 6²) / 4 = 36π/4 = 9π square units.

Thus, the area of Quarter Circle with radius 6 unit is 9π square units.

A quarter circle is one-fourth of a full circle. It resembles a slice of pie, that is divided into four equal parts. It includes a 90° angle and a curved edge, forming a right-angled sector. Calculating the area of a quarter circle is simple and useful in various applications. This article will guide you through the steps to determine the area, making it easy to understand and apply.