Area of a Quarter Circle

The circle is a shape with zero corners. It is symmetrical over any of its diameters. It gets divided into symmetrical parts when divided along the diameter. The symmetrical parts have equal areas. You must have noticed the way pizza is cut. Generally, pizza comes in a circular shape which is then further divided into 4,6, or 8 pieces. And all the pieces are of equal area. When a circle is divided along its diameter into four equal parts, we get 4 quarter circles. As the four parts have equal area, the area of a quarter circle is \frac{1}{4}^{th} that of the circle.

How Much is a Quarter?

A quarter meaning in maths is \frac{1}{4}. A quarter of any quantity is \frac{1}{4}^{th} of the whole quantity. So when you are talking about a quarter circle, it is \frac{1}{4}^{th} of the circle i.e. one-fourth of a circle.

A Quarter of Different Numbers

To find the quarter of any number, we divide the number by 4.

1. Quarter of 100

A quarter of 100 means, we need to find the value of \frac{1}{4}^{th} of 100. For this, we need to divide the 100 by 4.

A quarter of 100 = \frac{1}{4}*100

A quarter of 100 = 25

2. Quarter of 500

We need to find \frac{1}{4}^{th} of 500.

A quarter of 500 = \frac{1}{4}*500

A quarter of 500 = 125

What is an Area of a Quarter Circle?

The area of any is the amount of a plane enclosed by it. In the context of 2D figures, it is the play bounded by the boundary of the shape. When you're talking about 3D figures, surface area forms the boundary of the shape.

The area of a circle is given by the formula \pi r^{2}. Here 'r' is the radius of the circle.

Area of a quarter circle =\frac{1}{4} Area of a circle

=\frac{1}{4} \pi r^{2}

What is the Circumference of a Quarter Circle?

The circumference of a circle is the curve length or perimeter of the circle. When we find the circumference we get the value of the border of the circle. When a circle is divided into 4 equal parts, its circumference gets divided into four parts too.

Circumference of the circle is given by the formula 2\pi r. Here, 'r' stands for the radius of the circle.

Circumference of a quarter circle = \frac{1}{4} circumference of a circle

=\frac{1}{4}*2\pi r

=\frac{1}{2}*\pi r

The circumference of a quarter circle is \frac{1}{2}*\pi r

Examples

1. What is the value of a quarter to 2?

Quarter to 2 means, we need to find \frac{1}{4}^{th} of the number 2.

Quarter to 2 = \frac{1}{4}*2

= \frac{1}{2}

2. What is the area of a quarter of a circle having a radius of 8 cm?

The area of a quarter circle formula is \frac{1}{4} \pi r^{2}.

Area =\frac{1}{4} \pi r^{2}\\

\\

Area =\frac{1}{4} \pi (8)^{2}\\

\\

Area =\frac{1}{4} \pi(64) \\

\\

Area = 16\pi

3. A pizza has a total area of 76 sq.cm. It is divided into four equal parts. Find the area of each quarter.

The total area of pizza = 76 sq. cm

Area of each quarter = \frac{1}{4} * 76 \\

= 19sq. cm

The area of each pizza piece is 19 sq.cm.

4. Find the circumference of a circle having a quarter of the circumference 20cm

The circumference of a quarter of a circle is 20cm.

Circumference of circle = 4 * 20

= 80cm

5. What is the value of the area of a quarter circle whose circumference is \pi ?

The formula for the circumference of a quarter circle is \frac{1}{2}\pi r \\

Circumference = \frac{1}{2}\pi r \\

\pi = \frac{1}{2} \pi r \\

\\

r = 2

The formula for the area of a quarter circle is \frac{1}{4} \pi r^{2}

Area = \frac{1}{4} \pi r^{2} \\

Area = \frac{1}{4} \pi (2)^{2}

\\

Area = \frac{1}{4} \pi (4)

\\

Area = \pi