where
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

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

Answer: Area of circle
= π r^{2} = 3.14 × (4 × 4)
= 50.24 mm^{2}

Example Two - Lotus Lily 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.)

Answer: Area of circle
= π r^{2} = 3.14 × (15 × 15)
= 706.5 cm^{2}

Example Three - Lampshade Fabric

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.)

Answer: Area of larger circle
= π R^{2} = 3.14 × 10 × 10
= 314 cm^{2}

Area of smaller circle
= π r^{2} = 3.14 × 5 × 5
= 78.5 cm^{2}

Area of whole annulus
= 314 - 78.5
= 235.5 cm^{2}

Area of 200 degrees of annulus
= (200° ÷ 360°) × 235.5
= 130.8 cm^{2}

Questions

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

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.