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The Circumference of a Circle

The Circumference of a Circle. How many times does the diameter fit around the circumference? Choose your number. 1. 1½ . 2 . 2½ . 3 . 3½ . 4 . d. diameter(d). In terms of the radius:. radius. C =? . Circumference (C).  =. 1. 2. C =2 r. 3. The Circumference of a Circle.

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The Circumference of a Circle

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  1. The Circumference of a Circle How many times does the diameter fit around the circumference? Choose your number. 1 1½ 2 2½ 3 3½ 4 d diameter(d) In terms of the radius: radius C =? Circumference (C)  = 1 2 C =2r 3

  2. The Circumference of a Circle It’s the same for all circles!

  3. The Circumference of a Circle Find the circumference of the following circles. 1 2 8 cm 9.5 cm C =d C =2r C =d C=  x 8 C = 25.1 cm (1 dp) C =d C=  x 9.5 C = 29.8 cm (1 dp)

  4. The Circumference of a Circle Find the circumference of the following circles. 4 3 3 mm C =d 2.1 m C =2r C =2r C = 2 x  x 3 C = 18.8 mm(1 dp) C = 2r C = 2 x  x 2.1 C = 13.2 m(1 dp)

  5. Find the circumference of the tyre and steering wheel. 7.5 cm 23 cm C =2r C = 2 x  x 7.5 C = 47.1 cm(1 dp) C =d C=  x 23 C = 72.3 cm (1 dp)

  6. The Circumference of a Circle Find the perimeter of the following semi-circles. 1 2 8 cm 9.5 cm C =d C =2r Perimeter =½d + d = ½ x  x 9.5 + 9.5 = 24.4 cm (1 dp) Perimeter =½d + d = ½ x  x 8 + 8 = 20.6 cm (1 dp)

  7. The Circumference of a Circle Find the perimeter of the ¼ and ¾ circles. 3 4 8.5 cm 6 cm C =d C =2r Perimeter =¾(2r) + 2r = ¾ x 2 x  x 8.5 + 2 x 8.5 = 57.1 cm (1 dp) Perimeter =¼(2r) + 2r = ¼ x 2 x  x 6 + 2 x 6 = 21.4 cm (1 dp)

  8. C =d C =2r The Circumference of a Circle Find the diameter/radius of the following circles. 5 6 C = 25 cm find the diameter. C = 30 cm find the radius. 2r = 30 r = 30/(2) r = 4.8 cm (1 dp) d = 25 d = 25/ d = 8.0 cm (1 dp)

  9. The Area of a Circle Transform 4 Sectors

  10. Transform 8 Sectors The Area of a Circle

  11. Transform 16 Sectors The Area of a Circle

  12. As the number of sectors  , the transformed shape becomes more and more like a rectangle. What will the dimensions eventuallybecome? Transform ? 32 Sectors ? Remember C = 2πr πr ½C r A = πr x r = πr2

  13. A =r2 The Area of a Circle Find the area of the following circles. 1 2 8 cm 9.5 cm A =r2 A =  x 82 A = 201.1 cm2 (1 dp) A =r2 A =  x 9.52 A = 283.5 cm2 (1 dp)

  14. The Area of a Circle A =r2 Find the area of the following circles. 3 4 6 mm 2.4 m A =r2 A =  x 32 A = 28.3 mm2 (1 dp) A =r2 A =  x 1.22 A = 4.5 m2 (1 dp)

  15. Find the area of the clock face and radar screen. A =r2 12 cm 60 cm A =r2 A =  x 122 A = 452.4 cm2 (1 dp) A =r2 A =  x 302 A = 2827 cm2 (nearest cm2)

  16. A =r2 The Area of a Circle Find the area of the following semi-circles. 1 2 8 cm 9.5 cm A =½r2 = ½ x  x 4.752 = 35.4 cm2 (1 dp) A =½r2 = ½ x  x 42 = 25.1 cm2 (1 dp)

  17. The Area of a Circle A =r2 Find the area of the ¼ and ¾ circles. 3 4 8.5 cm 6 cm A =¾r2 = ¾ x  x 8.52 = 170.2 cm2 (1 dp) A =¼r2 = ¼ x  x 62 = 28.3 cm2 (1 dp)

  18. The Area of a Circle A =r2 Find the radius/diameter of the following circles. 6 5 A = 25 cm2 find the diameter. A = 30 cm2 find the radius. r2 = 25 r2 = 25/ r = (25/) r = 2.82 d = 2 x 2.82 = 5.6 cm 1dp r2 = 30 r2 = 30/ r = (30/) r = 3.1 cm 1dp

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