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Spring Board

Learn about circles, their components (circumference, diameter, radius), and how to find circumference and area using formulas.

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Spring Board

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  1. Spring Board Geometry – Circles

  2. What is a Circle? • Circlesare shapes made up of all pointsin a plane that are the same distancefrom a pointcalled the center. • Look at this example of a circle: circumference - the distance around a circle center diameter – the distance across a circle through its center radius – the distance from the center to any point on a circle

  3. What Do You Need to Know About Circles? • What is the distance around the circle? • How much space is inside the circle?

  4. What Do You Need to Know About Circles? • The distance around the circle is called the circumference. • The space is inside the circle is called the area.

  5. What is Unique About Circles? • The circumferenceofeverycircle is approximately three times longerthan its diameter! • This relationship ( ) is where πor pi comes from.

  6. What is Unique About Circles? • To find the circumferenceor area of a circle, you must usethis 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. How Do You Find Circumference? • You will always be given the circle’s diameter or the radius. • Your answer will be a linearmeasurement. • The radius is always½ of the diameter. • The diameter is alwaystwo 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. How Do You Find Circumference? • The circumference formulas are found on the key of the FCAT Reference Sheet.

  9. How Do You Find Circumference? • Choose the correct formula for circumference. Use this formula if you have diameter (d) Use this formula if you have radius (r)

  10. How Do You Find Circumference? • Write the circumferenceformula exactly as it appears on the FCAT Reference Sheet. • Rewrite the circumferenceformula substituting the values that you know. • Solve one step at a time rewriting after each step. C = Πd C = 3.14 × 12 A = 28.26 meters 9 meters

  11. How Do You Find Circumference? • Write the circumferenceformula exactly as it appears on the FCAT Reference Sheet. • Rewrite the circumferenceformula substituting the values that you know. • Solve one step at a time rewriting after each step. C = 2Πr C = 2 × 3.14 × 12 A = 75.36 meters

  12. How Do You Solve for a Missing Measurement? • Follow the same set of steps as before! • Write the circumferenceformula exactly as it appears on the FCAT Reference Sheet. • Rewrite the circumferenceformula substituting the values that you know. • Solve one step at a time rewriting after each step.

  13. How Do You Solve for a Missing Measurement? • Solve the following problem: • Find the diameterof a basketball hoop with a circumference of 56.52 inches. Use 3.14 for Π. C = Πd 56.52 = 3.14 × d Divide by 3.14 on both sides to undo the multiplication! 18 in. = d

  14. Find the Circumference of the Semi-Circles. One is on the left. 50 m 14 m One is on the right. Note: Use for Π.

  15. Find the Circumference of the Semi-Circles. C = Πd C = × 14 C = × C = × C = C = 44 meters 50 m 14 m Since you are finding two halves, you can find one whole instead!

  16. How Do You Find the Area? • 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 always½ of the diameter or r = d ÷ 2. • The diameter is equal to circumferencedivided bypi or 3.14. Or d = • Sometimes you are given radius. This means less work!!

  17. Find Area of a Circle • Select the correct area formula:

  18. Find Area of a Circle • 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 = Πr2 A = 3.14 × r × r A = 3.14 × 12 × 12 A = 3.14 × 144 A = 452.16 mm2 12 mm

  19. Find Area of a Circle • 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 = Πr2 A = 3.14 × r × r A = 3.14 × 3 × 3 A = 3.14 × 9 A = 28.26 ft2 r = d ÷ 2 r = 6 ÷ 2 r = 3 6 feet

  20. Find Area of a Semi-Circle • 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. Find Area of a Semi-Circle 4 inches

  22. Find Area of a Semi-Circle • 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. Why is Area in Square Units? • Remember that the shapes have two dimensions. • When you multiply one measurementby another measurement you end up with square units. • For Example: • Square Feet • ft2 • Square Inches • in2 • Square Centimeters • cm2

  24. Time to Practice • Remember to use the FCAT Reference Sheet:

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