Examples of Area Calculation
Example 1: What is the area of a quarter circle in square meters if its radius is 8 meters?
Solution
If the radius of a quarter circle is 8 meters, the area of the quarter circle can be calculated using the formula: Area = (1/4) πr2.
Substituting the given value, we get
Area = (1/4) x π x 82 = (1/4) x π x 64 = 16π.
Therefore, the area of the quarter circle is 16π square meters.
Example 2: In a yard, there is a flower bed that is 5-feet across and made like a quarter circle. How many square feet does this flower bed cover?
Solution:
The area of a quarter-circle shaped flower bed with a radius of 5 feet can be calculated similarly.
Using the formula Area = (1/4) πr2, we get
Area = (1/4) x π x 52 = (1/4) x π x 25 = 6.25π.
Therefore, the area of the flower bed is 6.25π square feet.
Example 3: An artist is painting a picture that is 10 meters across and in the shape of a quarter circle. How big will the painting be in square meters?
Solution:
For the mural with a radius of 10 meters, the area can be found using the formula
Area = (1/4) πr2.
Substituting the given value, we get
Area = (1/4) πr2 = (1/4) x π x 100 = 25π.
Thus, the area of the mural is 25π square meters.
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
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