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Shape and Space

Shape and Space. Circles. Let us define Circle. A ___________is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center.

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Shape and Space

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  1. Shape and Space Circles

  2. Let us define Circle • A ___________is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center. • A circle is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center.

  3. Radius is the distance from the center to the edge of a circle. Radius is half of the diameter

  4. Diameteris a segment that passes through the center and has its endpoints on the circle. The diameter is twice the length of the radius

  5. The value of π = 3.141592653589793238462643383279502884197169 39937510582097494459230781640628620899862803482 53421170679821480865132823066470938446095505822 31725359408128481117450284102701938521105559644 62294895493038196 (to 200 decimal places)! We use the symbol π because the number cannot be written exactly.

  6. In circles the AREA is equal to 3.14( ) times the radius (r) to the power of 2. Thus the formula looks like: A= r2 In circles the circumference is formula looks like: 2 r The circumference of a circle is the actual length around the circle which is equal to 360°. πis equal to 3.14.

  7. The circumference of a circle Use π = 3.14 to find the circumference of this circle. R = 4 C = 2πr 8 cm = 2 × 4 = 8π

  8. The circumference of a circle 9 m 4 cm 58 cm Use π = 3.14 to find the circumference of the following circles: C = 2πr C = 2πr = 2 × 2 = 2 × π × 9 = 4πcm = 18πm 24mm C = 2πr C = 2πr = 2 × 12 = 2 × π × 58 = 12πmm = 116πcm

  9. 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

  10. Area of a circle

  11. The circumference of a circle Use π = 3.14 to find the area of this circle. 4 cm A = πr2 = π × 4 × 4 = 16π cm2

  12. 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 = π × 22 = π × 52 = 4π cm2 = 25π m2 A = πr2 A = πr2 = π × 232 = π × 392 = 529π mm2 = 1521π cm2

  13. 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 12cmand the area of a rectangle of width 6cm and length 12cm. Area of circle = π × 62 12 cm 6 cm = 36π cm2 Area of rectangle = 6 ×12 = 78 cm2 Total area = 36π + 78

  14. Finding the radius given the circumference C = = 2π 12 6 π 2 × π 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 = ?

  15. 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. 14 cm 6 cm Perimeter = 14 x 6 Circumference = 2πr

  16. 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 = 2πr and π = 3.14, The circumference of the wheel = π × 50 = 157cm 50 cm

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