Circle Study Guide
Definition
A circle is a closed curve where all points are equidistant from the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter.
Key Concepts
- Radius: The distance from the center of the circle to any point on the circle.
- Diameter: The distance across the circle passing through the center, and it is twice the length of the radius.
- Circumference: The perimeter of the circle, given by the formula C = 2πr or C = πd, where r is the radius and d is the diameter.
- Area: The space enclosed by the circle, given by the formula A = πr2.
Formulas
Here are the key formulas related to circles:
- Circumference: C = 2πr or C = πd
- Area: A = πr2
Practice Problems
1. Find the circumference of a circle with radius 5 cm.
2. What is the area of a circle with diameter 12 m?
3. If the circumference of a circle is 31.4 cm, find its radius.
4. A circle has an area of 64π square units. Find its radius.
Solution
1. Circumference = 2πr = 2 * 3.14 * 5 = 31.4 cm
2. Radius = d/2 = 12/2 = 6 m, Area = πr2 = π * 62 = 36π square meters
3. Circumference = 2πr, 31.4 = 2 * 3.14 * r, r = 31.4 / (2 * 3.14) = 5 cm
4. Area = πr2, 64π = πr2, r2 = 64, r = 8 units
Conclusion
Understanding the concepts of radius, diameter, circumference, and area of a circle is essential for solving problems related to circles. Practice using the formulas and solving problems to improve your skills in this topic.
[Circle] Related Worksheets and Study Guides:
.◂Math Worksheets and Study Guides Seventh Grade. Plane Figures: Closed Figure Relationships
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