Area Of Circle

The formula is:

Area of Circle = π r2

π, pi is a constant, approximately 3.14
r is the radius

Take care to use the Radius and not the Diameter in this rule.

Example One - Contact Lens Size

Diagram of human eyes radius

A contact lens has a radius of 4 mm. What is its area?
(Assume the surface is flat and that π is 3.14.)

Area of circle
= π r2
= 3.14 × (4 × 4)
= 50.24 mm2

Example Two - Lotus Lily Leaf

Diagram of diameter of lotus leaf

Plant leaves use sunshine, carbon dioxide and water to photosynthesize and make oxygen and sugar. This lily leaf has a diameter of 30 cm. What is the area to be available for photosynthesis?
(Use π = 3.14.)

Area of circle
= π r2
= 3.14 × (15 × 15)
= 706.5 cm2

Example Three - Lampshade Fabric

Diagram of diameter of top and bottom lampshade

A lampshade design is made of an annulus with a central angle of 160 degrees. The diameter of the smaller circle is 10 cm. The diameter of the larger circle is 20 cm. What area of fabric is used in the lampshade? (Use π = 3.14.)

Area of larger circle
= π R2
= 3.14 × 10 × 10
= 314 cm2

Area of smaller circle
= π r2
= 3.14 × 5 × 5
= 78.5 cm2

Area of whole annulus
= 314 - 78.5
= 235.5 cm2

Area of 200 degrees of annulus
= (200° ÷ 360°) × 235.5
= 130.8 cm2


Find these areas. Use the ∏ button on your calculator.

Q1. A circle whose radius is 30 m
Q2. A circle with a diameter of 40 cm
Q3. A 120 degrees sector whose radius is 9 cm

A1. 2827.43 m2
A2. 1256.64 cm2
A3. 84.82 cm2

Did You Know That...?

Crop circles in a field

Crop circles are flattened areas of wheat fields formed by tying a rope to a central post (or using GPS), marking the circumference and slashing the inside crop. There are also conspiracy theories that they are made by "alien" spacecraft. In recent years, enterprising farmers with a sense of humour and an eye on their bank accounts have created crop circles for advertising companies.