Formulas Related to Quarter Circle

Below is a list of all the formulas related to the quarter circle:

Property	Formula
Arc Length (s)	¼ × Circumference (s = ¼ × πr)
Area (A)	¼ × πr²
Central Angle (θ)	90° (in degrees) or π/2 radians
Chord Length (c)	√(2r²)
Sector Area (A_sec)	½ × r² × θ
Segment Area (A_seg)	Sector Area – Area of triangle formed by radii and chord
Perimeter (P)	Arc Length + 2 × r

Area of a Quarter Circle

Area of a quarter circle is defined as the amount of space enclosed by one-fourth of a full circle. For a full circle, its area is equal to pi times the square of the radius (Area =πr² ).Therefore, the formula for the area of a quarter circle is:

Area of Quarter Circle = 1/4 πr²

The area of a quarter circle can also be calculated using different formulas based on the diameter, Since the diameter is twice the radius (d = 2r), the formula can be written as:

Area = (1/16) x π x d²

Example: Calculate the are of the quarter circle if the radius (r) is 4 units.

Solution:

Area of quarter circle = 1/4 πr²

Square the radius: 4 x 4 = 16

Multiply by π: 16 x π ≈ 16 x 3.14159 ≈ 50.27

Divide by 4: 50.27 / 4 ≈ 12.57

So, the area of the quarter circle is approximately 12.57 square units.

Perimeter of Quarter Circle

To find the perimeter of a quarter circle, you add the length of the curved part (arc) and the two straight sides. One-fourth of the circumference of a full circle (since a quarter circle is a fourth of a full circle) plus the length of the radius twice. The formula for the perimeter of a quarter circle with radius “r” is:

Perimeter = Half the circumference (πr/2) + 2 times the radius (2r)

Perimeter of Quarter Circle = πr/2 + 2r

Centroid of quarter circle

The centroid of a quarter circle circle with a radius of ( r ) is at (4r/3π, 4r/3π). From here, the calculation reveals that the centroid is 4r/3π units in both the x and the y direction from the origin; the origin is the point where the two radii are perpendicular to each other.

Quarter Circle

Quarter circle is an element of a circular shape that occupies one-fourth of the circle’s perimeter edge and has the same ratio in terms of the area, forming a right angle with the adjacent plane.

This article provides a background on the quarter circle by discussing its formulas and properties as well as real-life uses and gives examples about calculating the area and perimeter of the figure, and problems to solve for practice.

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