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Shape and Space

Shape and Space. Circles. The value of π. π = 3.141592653589793238462643383279502884197169 39937510582097494459230781640628620899862803482 53421170679821480865132823066470938446095505822 31725359408128481117450284102701938521105559644 62294895493038196 (to 200 decimal places)!.

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Shape and Space

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  1. Shape and Space Circles

  2. The value of π π = 3.141592653589793238462643383279502884197169 39937510582097494459230781640628620899862803482 53421170679821480865132823066470938446095505822 31725359408128481117450284102701938521105559644 62294895493038196 (to 200 decimal places)! For any circle the circumference is always just over three times bigger than the radius. The exact number is called π (pi). We use the symbol π because the number cannot be written exactly.

  3. Approximations for the value of π When we are doing calculations involving the value π we have to use an approximation for the value. Generally, we use the approximation 3.14 We can also use the π button on a calculator. When a calculation has lots of steps we write π as a symbol throughout and evaluate it at the end, if necessary.

  4. The circumference of a circle circumference π = diameter C π = d For any circle, or, We can rearrange this to make a formula to find the circumference of a circle given its diameter. C = πd

  5. Circle circumference and diameter

  6. The circumference of a circle Use π = 3.14 to find the circumference of this circle. C = πd 8 cm = 3.14 × 8 = 25.12 cm

  7. Finding the circumference given the radius The diameter of a circle is two times its radius, or d = 2r We can substitute this into the formula C = πd to give us a formula to find the circumference of a circle given its radius. C = 2πr

  8. The circumference of a circle 9 m 4 cm 58 cm 23 mm Use π = 3.14 to find the circumference of the following circles: C = πd C = 2πr = 3.14 × 4 = 2 × 3.14 × 9 = 12.56 cm = 56.52 m C = πd C = 2πr = 3.14 × 23 = 2 × 3.14 × 58 = 72.22 mm = 364.24 cm

  9. Finding the radius given the circumference C = 2π 12 2 × 3.14 Use π = 3.14 to find the radius of this circle. C = 2πr 12 cm How can we rearrange this to make r the subject of the formula? r = ? = 1.91 cm (to 2 d.p.)

  10. Find the perimeter of this shape Use π = 3.14 to find perimeter of this shape. The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm. 13 cm 6 cm Perimeter = 3.14 × 13 + 6 + 6 = 52.82 cm

  11. Circumference problem The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 1 km? Using C = πd and π = 3.14, The circumference of the wheel = 3.14 × 50 = 157 cm 1 km = 100 000 cm 50 cm The number of complete rotations = 100 000 ÷ 157 = 637

  12. Formula for the area of a circle We can find the area of a circle using the formula Area of a circle = π×r×r or radius Area of a circle = πr2

  13. Area of a circle

  14. The circumference of a circle Use π = 3.14 to find the area of this circle. 4 cm A = πr2 = 3.14 × 4 × 4 = 50.24 cm2

  15. Finding the area given the diameter d r = 2 πd2 A = 4 The radius of a circle is half of its radius, or We can substitute this into the formula A = πr2 to give us a formula to find the area of a circle given its diameter.

  16. The area of a circle 2 cm 10 m 78 cm 23 mm Use π = 3.14 to find the area of the following circles: A = πr2 A = πr2 = 3.14 × 22 = 3.14 × 52 = 12.56 cm2 = 78.5 m2 A = πr2 A = πr2 = 3.14 × 232 = 3.14 × 392 = 1661.06 mm2 = 4775.94 cm2

  17. Find the area of this shape Use π = 3.14 to find area of this shape. The area of this shape is made up of the area of a circle of diameter 13 cm and the area of a rectangle of width 6 cm and length 13 cm. Area of circle = 3.14 × 6.52 13 cm 6 cm = 132.665 cm2 Area of rectangle = 6 × 13 = 78 cm2 Total area = 132.665 + 78 = 210.665 cm2

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