Area of a Quarter Circle

Area of a quarter circle is one-fourth part of the whole area of the circle. When a circle is divided into four equal parts, each part is called the quarter of a circle. Each quarter is called the quadrant of the circle. So, the area of a quarter circle is times of area of the circle.

What is the area of a quarter circle?

A circle is a geometric figure that traces the path of all those points, which is equidistant to a unique point called the centre of the circle. A quarter of a circle is one-fourth part of the whole circle. Therefore, the area of a quarter circle is the fourth part of the whole area of a circle.

The formula for the area of a quarter circle using radius

If a circle has a length of radius r, then the area of the circle, A = r²

Then, the area of a quarter circle = times of A

= ¼ × πr² = πr²/4

The formula for the area of a quarter circle using the diameter

If the length of the radius is r, then the length of the circle’s diameter, d = 2r, that is, r = d/2.

Then, the area of circle = π(d/2)² = πd²/4

Area of a quarter circle = ¼ × π(d/2)² = πd²/16

Area of a quarter circle related articles

• Circumference of a circle
• Circle and its parts
• Area of a circle
• Quadrants

Solved examples on the area of a quarter circle

Example:

A circle has a radius of 14 cm, find the area of a quarter circle.

Solution:

Radius of circle = 14 cm

Area of a quarter circle = πr²/4 = 22/7 × ¼ × 14 × 14 = 154 cm²

Example:

A circle has a diameter of 32 cm, find the area of a quarter circle.

Solution:

Diameter of circle = 32 cm

Area of a quarter circle = πd²/16 = 22/7 × 1/16 × 32² = 201.14 cm²

Example:

A goat is tied to one corner of a square field. The length of the rope to which the goat is tied is 2m. Find how much area is available for the goat to graze.

Solution:

The grazing field will be a quarter of a circle of radius 2 m.

Area of grazing field = Area of a quarter circle with radius 2 m

= πr²/4 = 22/7 × ¼ × 2² = 22/7 ≈ 3.14 m²

Video Lessons on Circles