Quarter circles: calculate area, perimeter and radius

Key Notes :

What is a Quarter Circle?

A quarter circle is one-fourth of a full circle.

It looks like a “slice” of a circle, formed when a circle is divided into 4 equal parts.

Key Formulas

(a) Area of a Quarter Circle

A=1/4×πr²

(b) Perimeter of a Quarter Circle

The perimeter consists of:

• One arc length (¼ of the circumference),
• Two radii.

P=1/4×2πr+2r

P=1/2​πr+2r

(c) Radius from Area

If area of a quarter circle is given: r=√4A/π

Examples

Example 1: Area

Find the area of a quarter circle of radius 14 cm.

A=1/4πr²=1/4×22/7×14×14=154 cm²

Example 2: Perimeter

Find the perimeter of a quarter circle of radius 7 cm.

P=1/2πr+2r=1/2×22/7×7+14

P=11+14=25 cm

Example 3: Radius from Area

The area of a quarter circle is 19.625 cm². Find its radius (use π=3.14).

A=1/4πr2  ⟹  r2=4A/π

r²=4×19.625/3.14=25  ⟹  r=5 cm

Important Points

A quarter circle = 90° sector of a circle.

Always add 2 radii when finding the perimeter.

Units:

• Area → cm², m², etc.
• Perimeter → cm, m, etc.

Practice Questions

1. Find the area of a quarter circle with radius 21 cm.
2. Find the perimeter of a quarter circle with radius 14 cm.
3. A quarter circle has area 77 cm². Find its radius.
4. A wire is bent into the shape of a quarter circle of radius 28 cm. Find the length of the wire.
5. A quarter circular garden has a radius of 10 m. Find its area and perimeter.

Learn with an example

Let’s practice!🖊️