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Circumference of a Circle

Circumference of a Circle. Objective: Investigate & explain the relationships among radius, diameter, and circumference. Distance around a circle:. The distance around a circle is its circumference . For any circle, the circumference C, divided by the diameter, d, is approximately 3.

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Circumference of a Circle

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  1. Circumference of a Circle • Objective: Investigate & explain the relationships among radius, diameter, and circumference.

  2. Distance around a circle: • The distance around a circle is its circumference. • For any circle, the circumference C, divided by the diameter, d, is approximately 3.

  3. The circumference of a circle is also the perimeter of the circle! • Circumference divided by diameter equals 3. • or C/d = 3

  4. The ratio C/d = π • Pi is a decimal that never repeats and never terminates. • π cannot be written as a fraction, • For this reason, we call π an irrational number.

  5. C = πd • Since the diameter is twice the radius, the circumference is also π multiplied by 2r. • We write: C = π x 2r, or • C = 2πr

  6. When we know the radius or diameter • of a circle, we can use one of the formulas to find the circumference of a circle.

  7. The face of a toonie has a radius of 1.4 cm • To find the diameter of the face: • The diameter = 2r, where r is the radius. • Substitute: r = 1.4; d = 2x1.4 • =2.8 • The diameter is 2.8 cm.

  8. Circumference is a length, so its units are units of length such as centimetres, metres, or millimetres.

  9. To find the circumference of the face: • C = πd • Substitute d = 2.8 • C = π x 2.8 • = 8.796 • = 8.8 cm to one decimal place

  10. or… • C = 2πr • Substitute: r = 1.4 • C = 2 x π x 1.4 • = 8.796 • = 8.8 cm to one decimal place.

  11. We can estimate to see if the answer is reasonable: • The circumference is approx. 3 times the diameter. • 3 x 2.8 cm = 3 x 3 cm • = 9 cm • The circumference is approximately 9 cm. The calculated answer is 8.8 cm, so this answer is reasonable.

  12. When we know the circumference, we can use a formula to find the diameter.

  13. C = πd • To isolate d (get d by itself), divide each side by π • C/π = πd/π • C/π = d • So, d = C/π

  14. An above-ground circular swimming pool has a circumference of 12 m. • Calculate the diameter and radius of the pool. • Give answers to the two decimal places. • Check if the answers are reasonable.

  15. Solution • The diameter is: d = C/π • Substitute: C = 12 • d = 12/π - use a calculator; do not clear your calculator • = 3.8197 • The radius is 1/2 the diameter, or r = d/2 • Divide the number in the calculator display by 2.

  16. Solution continued… • r = 1.9099 • The diameter is 3.82 m to two decimal places. • The radius is 1.91 to two decimal places.

  17. Since the circumference is approx. 3 times the diameter, the diameter is about 1/3 the circumference. • One=third of 12 m is 4 m. So the diameter is about 4 m. • The radius is 1/2 the diameter. 1/2 of 4 m is 2 m. • The radius of the pool is about 2 m. • Since the calculated answers are close to the estimates, the answers are reasonable.

  18. Practice, pages 136-137 • #s 1a, 2a, 3-8. • This is due and will be corrected/handed in on Wednesday, March 12:)

  19. The 2 circles are congruent • Remember that congruent shapes are identical. They are shapes that match exactly. • A circle with a radius of 5 cm has a diameter of 10 cm. • What is the diameter of a circle that has a radius of 3 cm? What is the radius of a circle that has a diameter of 24 cm?

  20. How to use a protractor to measure angles. • Video

  21. Assignment • Because of skiing tomorrow, this assignment is due on Monday, March 10, 2014. • We will correct at the beginning of class. • Pages 131-132, #s 1-6

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