Area and Circumference of a Circle

2 Definitions A circle is the set of all points in a plane that are the same distance from a fixed point called the center of the circle. A radius of a circle is a line segment extending from the center to the circle. A diameter is a line segment that joins two points on the circle and passes through the center. radius center diameter

A line segment that joins any point on the circle to its center is called a radius. The radius is ½ way across the circle. Radius Center

A line segment that joins any two points on the circle and passes through its center is called a diameter. The diameter is all the way across the circle, which means it’s TWICE the radius. Diameter Center

You try: Radius = ____________ Diameter = ___________ Radius = ____________ Diameter = ___________ 26 cm 4.5 mm 9 mm 26 cm 13 cm

The distance around a circle is called its circumference. Centre

What is ? The ratio of the circumference of a circle to its diameter. Circumference diameter

3.14 and Beyond… The numbers to the right of the 3 never repeat in a pattern. For any circle, we use the approximation 3.14 for π

Circumference Formulas C = π ∙ d C = 2∙ π ∙ r When the diameter is given, use the following formula: When the radius is given, use the following formula:

The circumference of a circle Use π = 3.14 to find the circumference of the following circles: C = πd 4 cm = 3.14 × 4 = cm C = 2 πr 9 m = 2 × 3.14 × 9 = m C = πd 23 mm = 3.14 × 23 = mm C = 2 πr 58 cm = 2 × 3.14 × 58 = cm

How in the world would you find the area of a circle?

Remember! Area is always measured in square units.

Let’s look at a rectangle. Area = (Length)(Width) (Hint: you’re counting the number of squares inside of the rectangle) 2 4 A = L x W A = (4)(2) A = There are 8 squares in the rectangle.

Now consider a circle. Estimate the number of square units inside the circle. There are about 13 square units inside this circle. There are about 12 squares plus the 4 parts that are approximately of a square each

This is just an ESTIMATE though. How can we find the exact area? Area of a circle = π r 2 This will tell us exactly how many squares are inside the circle

Area of a Circle Curious to know why this formula works? Watch this video on your own.

The area of a circle Use π = 3.14 to find the area of the following circles: A = πr 2 2 cm = 3.14 × 2 2 = cm 2 A = πr 2 10 m = 3.14 × 5 2 = 78.5 m 2 A = πr 2 23 mm = 3.14 × 23 2 = mm 2 A = πr 2 78 cm = 3.14 × 39 2 = cm 2

Practice: Area and Circumference Worksheet