1. Circle Formulas Vocabulary: Circumference Radius Diameter Pi

2. Circle Formulas Circumference – the distance around the outside of a circle Radius – the distance from the center of a circle to any point on the outside Diameter – the distance from one side of the circle to another passing through the center Pi – a numerical constant approximately equal to 3.14 – represented by this symbol: π

5. If the diameter of a circle is 12, what is the radius?

6. The radius will always be ½ of the diameter, so the radius of the circle in this case is 6.

7. If the radius of a circle is 1.5, what is the diameter of the circle?

8. Diameter is always twice the radius, so the diameter of this circle would be 3.

9. Remember that pi is calculated using the ratio of the circumference to the diameter: Another way to say this would be: C÷D = π

10. Another way to say this would be: C÷D = π Using your algebra “juggling” skills, it should be clear why the formula to find the circumference of a circle is π times the diameter or: πD C÷D = π xD xD C = πD

11. Circumference Formula The circumference formula works just like the other geometric formulas you’ve learned – the only new thing is π, which, for the GED, is always equal to 3.14 What is the circumference of a circle with a diameter of 4?

12. Circumference Formula What is the circumference of a circle with a diameter of 4? Step 1 – Write the formula: C = πD Step 2 – substitute numbers for letters where possible: C = 3.14 x 4 Step 3 – Solve C = 12.56

13. Circumference Formula What is the circumference of a circle with a radius of 3 inches?

14. Circumference Formula What is the circumference of a circle with a radius of 3 inches? Step 1 - C = πD Step 2 – we need the diameter to go in place of the variable “D” – if the radius is 3, then the diameter is 6, so: C = 3.14 x 6 Step 3 – C = 18.84

15. Circumference Formula If necessary, you should also be able to find the diameter of a circle if you’re given the circumference. What is the diameter of a circle with a circumference of 25.12?

16. Circumference Formula What is the diameter of a circle with a circumference of 25.12? Step 1 - C = πD Step 2 – 25.12 = 3.14 x D Step 3 – 25.12 = 3.14 x D ÷3.14 ÷3.14 8 = D

17. Area Formula

18. The formula to find the area of a circle, or the number of square units that would fit inside it, is: Pi times the radius squared A = πr 2 The area formula works like all the others, just remember your order of operations.

19. Area Formula Pi times the radius squared A = πr 2 What is the area of a circle with a radius of 5cm?

20. Area Formula What is the area of a circle with a radius of 5? Step 1 - A = πr 2 Step 2 – A = 3.14 x 5 2 Step 3 - A = 3.14 x 5 2 A = 3.14 x 25 A = 78.5 cm 2 *Note that area is measured in square units

21. Area Formula What is the area of a circle with a diameter of 12 feet?

22. Area Formula – What is the area of a circle with a diameter of 12 feet? Step 1 - A = πr 2 Step 2 – We need the radius, which is half of the diameter, so: A = 3.14 x 6 2 Step 3 - A = 3.14 x 6 2 A = 3.14 x 36 A = 113.04 square feet

23. Area Formula What is the area of this circle? 14 inches

24. Area Formula What is the area of this circle? Step 1 - A = πr 2 Step 2 – We need the radius, which is half of the diameter, so: A = 3.14 x 7 2 Step 3 - A = 3.14 x 7 2 A = 3.14 x 49 A = 153.86 square inches 14 inches

25. Volume Formula A cylinder is a 3 dimensional container with the top and bottom circular. It’s another word for a tube shape. On the GED, you might need to calculate the volume of a can or a barrel. Volume is measured in cubic units

26. Volume Formula The formula for volume of a cylinder is: radius V = πr 2 h height Notice that it’s the area formula times the height of the cylinder.

27. Volume Formula What is the volume of the cylinder?

28. Volume Formula Step 1: V =πr 2 h Step 2: V = 3.14 x 7 2 x 12 Step 3: V = 3.14 x 49 x 12 V = 1846.32 cubic inches or 1846.32 in 3

29. Volume Formula What is the volume of this cylinder?

30. Volume Formula Step 1: V =πr 2 h Step 2: V = 3.14 x 2.25 2 x 11.5 Step 3: V = 3.14 x 5.0625 x 11.5 V = 58.21875 cubic inches or 58.21875 in 3 If you get a problem like this one on the GED, it’s pretty safe to say it will be on the calculator-allowed section!

31. Circle Formulas Fill out the worksheets on pages 158 through the top of page 161 in the book. Check your answers using the key on BB.