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Circles

Circles. Pi = . Pi ( π ) is a Greek letter It is a number that goes on forever It is the ratio of a circles circumference to its diameter This number is shortened to 3.14 It has it’s own button on the calculator Pi day is on the 3 month and 14 th day March 14 th

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Circles

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  1. Circles

  2. Pi = • Pi (π) is a Greek letter • It is a number that goes on forever • It is the ratio of a circles circumference to its diameter • This number is shortened to 3.14 • It has it’s own button on the calculator • Pi day is on the 3 month and 14th day • March 14th • It is extremely important to Physics and engineering

  3. Circumference Animation

  4. The Circle • The circumference is the whole way around the circle • The diameter is the width of the circle going through the centre • The radius is halfthe width

  5. C =πd • I f you need to find the circumference of a circle you multiply the diameter by Pi • E.g. • Find the circumference of this circle (to 1 d.p.) • C = π x 7 • C = 22 cm 7cm

  6. Try these; • Find the circumference if: • The diameter is 12.6 cm? • The radius is 4.3 cm? • The radius is 1.6 cm? • Find the outer circumference of this roll of sticky tape: 3.4 1.7cm

  7. Answers • 39.6 cm • 27.0 cm • 10.1 cm • 21.4 cm

  8. Working backwards • If C =πd,then we can work out the diameter if we are given the circumference • E.g. C =πd 52= πd We need to divide 52 by π D= 16.6 cm Circumference= 52 cm

  9. Now try these; • Find the diameter if the circumference is; • 85 cm • 12.6 cm • 25.3 cm • Find the radius if the circumference is; • 200m • 400m

  10. Answers • 27.1 cm • 4 cm • 8 cm • 31.8 m • 63.7m

  11. Area Animation

  12. A =πr2 • Like most areas you need to multiply two sides together, this is where the r2 comes in, but for a circle you have to multiply this by pi • E.g. • Find the area of this circle: • A =πr2 • A =π x 7.42 • A = 54.8 xπ • A = 172.2cm2 7.4cm

  13. Try these; • Find the area if; • The diameter is 25.2 cm? • The diameter is 10 yards? • A CD is made from plastic. Find the area of plastic in this CD; 12 cm 1.5cm

  14. Answers • 498.8 cm2 • 78.5 yards2 • 111.3cm2

  15. Working backwards • If A =πr2 then you can find the radius if you have the area • E.g. • 500 = πr2 • Divide 500 byπ to find out what r2 is • 159.2 = r2 • This is not the radius, but the radius squared, so we need to square root our answer • R = 12.6 cm Area = 500 cm2

  16. Now try these; • Find the radius if the area is • 34 cm2 • 200mm2 • Find the circumference for both circles

  17. Answers • 3.3 cm • 8 mm • 20.7 cm • 50.3 cm

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