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.
Area of a Quarter Circle
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.
Table of Content
- What is a Quarter Circle?
- Properties of a Quarter Circle
- Area of a Quarter Circle Formula
- Derivation of the Formula
- Calculating the Area of a Quarter Circle
- Examples of Area Calculation
- FAQs on Area of a Quarter Circle