📖Definition
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.
📐Formula
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.
Calculate Circumference
Use C = 2πr or C = πd.
Calculate Area
Use A = πr². Remember to square the radius, not the diameter.
⚠️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
A circle has radius 7 cm. What is its diameter?
Answer: 14 cm
Find the circumference of a circle with diameter 10 m (use π = 3.14)
Answer: 31.4 m
A circle has area 78.5 cm². Find the radius (use π = 3.14)
Answer: 5 cm
Ready to Practice Circles?
Generate a personalized practice test with MathQuizily. Get instant PDF downloads with answer keys.