The area of a quarter circle signifies a unique portion of a full circular region, precisely one-fourth of the total space enclosed by the boundary of a complete circle. The other name of area of a quarter circle is area of a quadrant.
What is the area of a quarter circle?
A quarter circle is a geometric shape that represents one-fourth (1/4) of a full circle. It is obtained by taking a circle and dividing it into four equal parts by two perpendicular radii, creating a right angle at the center.
The area of a quarter circle, which is one of the four equal parts into which a full circle can be divided, can be defined as the space enclosed by its curved boundary. To calculate this area, you square the length of the radius, multiply it by the constant pi (approximately 3.14159), and then divide the result by 4.
The image below illustrates the division of a circle into four equal quarters.
- A quarter circle’s area is like a slice of pizza, one-fourth of the total pizza.
- It’s a quarter of the area enclosed by a full circle’s boundary.
- Just as a pizza slice is a part of the whole pizza, a quarter circle’s area is a part of the entire circle’s area, specifically one-fourth of it.
Area of Quarter Circle: Formula Using Radius
The area of quarter circle is simply square the radius, multiply it by pi, and then divide the result by 4 to calculate the area.
The formula for calculating the area of a quarter circle using the radius (r) is:
In this formula:
- A represents the area of the quarter circle.
- π is a mathematical constant, approximately equal to 3.14159.
- is the radius of the quarter circle, which is the distance from the center of the circle to its outer edge.
How It Works
Now, let’s see how this formula works in practice. Imagine you have a quarter circle with a radius of 5 units. To find its area:
- Square the radius: r2 = 52 = 25r
- Multiply the squared radius by π: 25 x π ≈ 78.54.
- Finally, divide this result by 4:78.54/4 = 19.64
So, the area of a quarter circle with a radius of 5 units is approximately 19.64 square units.
Area of a Quarter Circle: Formula Using Diameter
Calculating the area of a quarter circle using the diameter is a straightforward process. The formula for finding the area of a quarter circle with the diameter (D) is:
A = π /16 x D2
Here’s how this formula works:
- A: This represents the area of the quarter circle.
- π (pi): This mathematical constant is approximately equal to 3.14159 and is crucial in geometry for calculations involving circles.
- D: The diameter of the quarter circle, which is the distance across the circle passing through its center.
To calculate the area, follow these steps:
- Square the diameter: D2
- Multiply the squared diameter by π/16
How To Find the Area of a Quarter Circle
To find the area of a quarter circle, you can follow these steps:
Step 1: Measure the Radius or Diameter
First, you need to measure either the radius (the distance from the center to the outer edge) or the diameter (the distance across the circle passing through its center) of the quarter circle. Make sure your measurement is in the same units (e.g., inches, centimeters) for consistency.
Step 2: Use the Appropriate Formula
Using Radius (r):
- Square the radius (r2).
- Multiply the squared radius by π/4 to calculate the area (A).
Using Diameter (D):
If you have the diameter (D), you can use the formula:
A = π/16D2
- Square the diameter (D2).
- Multiply the squared diameter by π/16 to calculate the area (A).