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What Is the Circles?(With Examples)

A circle is a round shape where every point on the edge is the same distance from the center. This distance is called the radius. The diameter is twice the radius and passes through the center. Pi (π ≈ 3.14159) is the ratio of circumference to diameter.

Grades 6-7Key Stage 3 (Year 7-9)Årskurs 6-8Klasse 6-8

📖Definition

📐Formula

Area: A = πr²; Circumference: C = 2πr = πd

The radius (r) is the distance from center to edge. The diameter (d) is twice the radius. Circumference is the perimeter of a circle. Area is the space inside.

📝Step-by-Step Guide

Identify the Given Information

Determine if you have the radius, diameter, circumference, or area.

Convert Between Radius and Diameter

Remember: d = 2r, so r = d/2.

diameter = 2 × radius

Calculate Circumference

Use C = 2πr or C = πd.

C = 2πr = πd

Calculate Area

Use A = πr². Remember to square the radius, not the diameter.

A = πr²

⚠️Common Mistakes to Avoid

Confusing radius with diameter
Using diameter in the area formula instead of radius
Forgetting to square the radius for area
Confusing circumference with area
Not using the same units throughout

✏️Practice Problems

Easy

A circle has radius 7 cm. What is its diameter?

Answer: 14 cm

Medium

Find the circumference of a circle with diameter 10 m (use π = 3.14)

Answer: 31.4 m

Hard

A circle has area 78.5 cm². Find the radius (use π = 3.14)

Answer: 5 cm

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Area Perimeter Angles Pi (π)

Curriculum Alignment

CommonCore (7.G.B.4)KS3KMK

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