Circle

A circle is a closed curve in a plane that is made up of all points that are the same distance from a fixed point called the center. This distance is called the radius of the circle. The longest distance across a circle, passing through the center, is called the diameter. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Key Concepts

1. Radius: The distance from the center of the circle to any point on the circle.
2. Diameter: The distance across the circle passing through the center. It is equal to 2 times the radius (d = 2r).
3. Circumference: The distance around the circle. It is given by the formula C = 2πr or C = πd.
4. Area: The amount of space inside the circle. It is given by the formula A = πr².

Formulas

Circumference: C = 2πr or C = πd

Area: A = πr²

Practice Problems

1. Find the circumference of a circle with radius 5 units.
2. Find the area of a circle with radius 7 units.
3. If the diameter of a circle is 12 units, find the circumference and the area of the circle.

Answers

1. Circumference = 2π × 5 = 10π units
2. Area = π × 7² = 49π square units
3. Circumference = π × 12 and Area = π × 6²

Remember to use the correct units in your answers and always label your final answer appropriately. Good luck with your study!

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