1. Geometry – Circles

2.  Circles are shapes made up of all points in a plane that are the same distance from a point called the center.  Look at this example of a circle : circumference - the distance around a circle radius – the distance from the center to any point on a circle diameter – the distance across a circle through its center center

3.  What is the distance around the circle ?  How much space is inside the circle ?

4.  The distance around the circle is called the circumference.  The space is inside the circle is called the area.

5.  The circumference of every circle is approximately three times longer than its diameter!  This relationship ( ) is where π or pi comes from.

6.  To find the circumference or area of a circle, you must use this relationship or the value pi.  Pi 3.14 or  You may use whichever form you wish.  If your problem contains multiples of seven (7), it makes sense to use the fractional form of pi. ≈

7.  You will always be given the circle’s diameter or the radius.  Your answer will be a linear measurement.  The radius is always ½ of the diameter.  The diameter is always two times the radius. radius – the distance from the center to any point on a circle diameter – the distance across a circle through its center

8.  The circumference formulas are found on the key of the FCAT Reference Sheet.

9.  Choose the correct formula for circumference. Use this formula if you have diameter (d) Use this formula if you have radius (r)

10.  Write the circumference formula exactly as it appears on the FCAT Reference Sheet.  Rewrite the circumference formula substituting the values that you know.  Solve one step at a time rewriting after each step. C = Π d C = 3.14 × 12 A = 28.26 meters 9 meters

11.  Write the circumference formula exactly as it appears on the FCAT Reference Sheet.  Rewrite the circumference formula substituting the values that you know.  Solve one step at a time rewriting after each step. C = 2 Π r C = 2 × 3.14 × 12 A = 75.36 meters

12.  Follow the same set of steps as before!  Write the circumference formula exactly as it appears on the FCAT Reference Sheet.  Rewrite the circumference formula substituting the values that you know.  Solve one step at a time rewriting after each step.

13.  Solve the following problem:  Find the diameter of a basketball hoop with a circumference of 56.52 inches. Use 3.14 for Π. C = Π d 56.52= 3.14 × d Divide by 3.14 on both sides to undo the multiplication! 18 in. = d

14. 1.One is on the left. 2.One is on the right. Note: Use for Π. 14 m 50 m

15. 1.C = Πd 2.C = × 14 3.C = × 4.C = × 5.C = 6.C = 44 meters 14 m 50 m Since you are finding two halves, you can find one whole instead!

16.  You will always be given the circle’s diameter, radius, or its circumference.  You need to find the value of radius before you begin!  The radius is always ½ of the diameter or r = d ÷ 2.  The diameter is equal to circumference divided by pi or 3.14. Or d =  Sometimes you are given radius. This means less work!!

17.  Select the correct area formula:

18.  Write the area formula exactly as it appears on the FCAT Reference Sheet.  Rewrite the area formula substituting the values that you know.  Solve one step at a time rewriting after each step. A = Πr 2 A = 3.14 × r × r A = 3.14 × 12 × 12 A = 3.14 × 144 A = 452.16 mm 2 12 mm

19.  Write the area formula exactly as it appears on the FCAT Reference Sheet.  Rewrite the area formula substituting the values that you know.  Solve one step at a time rewriting after each step. A = Πr 2 A = 3.14 × r × r A = 3.14 × 3 × 3 A = 3.14 × 9 A = 28.26 ft 2 6 feet r = d ÷ 2 r = 6 ÷ 2 r = 3

20.  Write the area formula exactly as it appears on the FCAT Reference Sheet.  Rewrite the area formula substituting the values that you know.  Solve one step at a time rewriting after each step.  Divide your answer by 2! Note: You could also use the formula or

21. 4 inches

22.  Remember to multiply by ½ or divide by 2 !  Choose the formula that you feel the most comfortable using.  You are finding the area of one half of a circle!  You can use this same method to find the circumference of one half of a circle!

23.  Remember that the shapes have two dimensions.  When you multiply one measurement by another measurement you end up with square units.  For Example: Square Feet ft 2 Square Inches in 2 Square Centimeters cm 2

24. RRemember to use the FCAT Reference Sheet: