The Trojan War and The Iliad The gods

The Trojan War and The Iliad

• The gods Apollo and Poseidon built the city of Troy. • Priam, the King of Troy had a son named Paris. • A prophet foretold that Paris would destroy

Well maybe not. • But why did Troy stand for so long? • The pythagorean theorem! •

Circumference and Area of Circles

Parts of a Circle • Radius-Straight line from the middle to the outside of a circle

• Diameter-a line that cuts the circle in half from end to end

Circumference • Circumference is the distance around the circle. Like the perimeter.

Pi • Pie is a special number. It is the ratio of the circumference and the diameter

• Pi goes on forever!!!!!! • We approximate it using 3. 14

Finding Circumference

Finding Circumference 6 · 3. 14 = 18. 84 in. 6�� in. would be the exact answer, but we are going to estimate using �� = 3. 14

What if you have the radius? The radius is half of the diameter

How Would You Find the Diameter if You Only Had the Circumference? • It’s easy! • When given circumference, to find diameter just divide by pi.

Circumference = �� d 21. 98 = 3. 14 d C = 21. 98 cm

Circumference = �� d C = 37. 68 m

Circumference = �� d C = 47. 10 m

I thought penguins were smart?

Area of a Circle

Area of a Circle The Formula

Example 3. 14 · 36 = 113. 04 in²

Try

Try

What if you are given the diameter? • How can you find the radius if you only have the diameter? • The radius is half of the diameter • Diameter = 8 then radius =4

Radius = 3 Example

Try

Finding Radius and Diameter from Area • Just like you could find radius and diameter from circumference, you can find the radius and diameter from area by filling in known values and solving.

Example Area = �� r² Area = 78. 50 cm² Radius = Diameter =

Area = 314. 00 cm² Radius = Diameter =

Area = 200. 96 cm² Radius = Diameter =

Closure • What is the formula for finding the area of a circle?

Closure • How can you find the radius if you only have the diameter?

Closure • What is the diameter?

Closure • What is the radius?

Closure • What is circumference?

Closure • What is the relationship between the radius and the diameter?