Area of Quarter Circle

A quarter circle means 1/4^th of the total area of the Circle. When a circle is partitioned into four equal parts, each part is called the quarter of the Circle, and the quarter is referred to as the quadrant of the Circle.

$Area of Quarter Circle$

The area of the quarter circle is ¼ the of the area of the Circle

What is an Area of the Circle?

A circle is a geometrical figure in which the set of all points in the plane is equidistant from a given point called the centre. Area of the circle = πr²

Circle and its Related Term

The circles split the plane into three division

Interior of the Circle
Circle
Outside the Circle (exterior of the Circle)

Circular Region: The interior and the Circle comprise the circular region.

Diameter: Diameter is the chord that crosses through the Circle's centre. The diameter of the Circle is the longest chord of the Circle.

Properties of the Diameter

It has the same length.
It is twice the radius. This can be illustrated as. Assume 'D' be the diameter of the Circle and 'r' be the radius of the Circle, then the equation is given by;

D = 2r

Circumference/ Perimeter of the Circle: The complete Circle's length is called the Circle's circumference or the Circle's perimeter.

The Formula

Let us assume that if a circle has a radius r, then the area of the Circle is given by A=πr²

Then, the area of the quarter circle is given by: ¼πr²

Area of the Quarter Circle Using the Diameter

The diameter of the Circle is given by d = 2r

Therefore, the area of the quarter circle = ¼ π(d/2)²

Frequently Asked Question

Question: Determine the area of a quarter circle if the Circle has a radius of 7cm.

Ans: From the question, we know that

Radius = 7 cm

The area of the quarter circle =πr²/4
= 154/4
= 38.5 cm²

Question: What do you mean by the radius of the quarter circle?

Answer: The Circle's radius equals the radius of the quarter circle, which is the length of a segment from the center of the Circle to the outside edge.

Question: What do you understand by the area of the quadrant?

Ans: The area of a quarter circle, i.e., πr²/4 is equal to the area of the quadrant.

Question: How will you determine the area of the quarter circle when the perimeter/ circumference of the Circle is given?

Ans: Circumference of the Circle is given by:

C= 2πr

Where r = radius of the Circle

π = 22/ 7,

From the above formula, we can get the value of the radius

Put the value of the radius into the formula, i.e., $Area of Quarter Circle$ .

Question: The price for wiring a circular field is fixed at Rs 25 per meter, which is Rs 5000. The field is to be sold at the price of Rs 0.25 per m². Determine the cost of the field.