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Scale Factor and the relationship to area and volume

Scale Factor and the relationship to area and volume. GLE 0706.2.3 0706.4.3 SPI: 0706.2.7 0706.4.3. Remember these rules !!. If 2 shapes are similar, it is by multiplication. The number that we multiply by is the scale factor. Scale factor is the ratio of corresponding parts.

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Scale Factor and the relationship to area and volume

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  1. Scale Factor and the relationship to area and volume GLE 0706.2.3 0706.4.3 SPI: 0706.2.7 0706.4.3

  2. Remember these rules !! If 2 shapes are similar, it is by multiplication The number that we multiply by is the scale factor. Scale factor is the ratio of corresponding parts.

  3. Let’s review, what we know about similar shapes. x = 3.5cm x 1.75 cm 2.8 cm 5.6 cm 2.8 = 1.75 9.8 = 2.8 x 5.6 x 2.8 2.8

  4. Try again x = 2m 8 m x 6 m 1.5 m 6 = 8 12 = 6 x 1.5 x 6 6

  5. Remember: if shapes are similar it is because they are related by multiplication. If a shape doubles, the scale factor is 2; if the shape triples in size, the scale factor is 3, and so on.

  6. The second quadrilateral is twice as tall and twice as wide. 1.75 cm 2.8 cm 3.5 cm This means the scale factor is 2. 5.6 cm

  7. Scale factor and Area

  8. 1.75 cm The rule: to find the area of the second shape multiply the area of the first times the scale factor squared. 2.8 cm The scale factor is 2, so its square is 4… let’s test it. 3.5 cm 5.6 cm

  9. Since the scale factor is 2, the shape is twice as tall and twice as wide. test the rule Remember, you are using the scale factor to find area when you don’t know the length of all the sides. (l * w) scale factor2 1.75 x 2.8 x 22 1.75 cm 2.8 cm 1.75 x 2.8 x 4 = 3.5 cm 19.6 cm 2 Check yourself.. is that = to 5.6 x 3.5 ? 5.6 cm

  10. The second tripled in size, so the scale factor is 3 The area of the second: Area of first x 2 4 scale factor 6 5 10 x 32 10 x 9 = 90 Yes, ½ 15 * 12 = 90 Is this true if you use the formula ½ b x h 15

  11. The reason this works is because area is increased by length and width. If both dimensions are increased, you are square – ing.

  12. The second shape is 3x as big, so the scale factor is 3. 2m 6m 18m The area of the first times the Scale factor 2. 12 x 32 = 12 x 9 = 108m2

  13. If the scale factor is ½ what would be the area of the smaller? 10 cm remember Area of the first times the scale factor2 the rule 10 * 10 * (1/2)2= 100 * ¼ = 25 cm2

  14. Scale factor and volume

  15. Now let’s look at scale factor and volume. The rule is to multiply the volume of the known times the scale factor3. Remember you are increasing the length, width, and height of a shape, thus cube - ing.

  16. 5 cm 3 cm 10 cm 30 cm The scale factor is 3, because the size has tripled. What is the volume of the larger prism? Hint: volume of small x scale factor3 150 x 33= 150 x 27 = 4050 cm3

  17. 5 m 5 m 30 m 10 m What is the scale factor? ½ the shape is reduced by 2 What is the volume of the small? Hint: volume of small x scale factor3 750 x (1/2)3= 750 x 1/8 = 93.75 cm3

  18. Now Check yourself !! Answers: 600 135 200

  19. Now Check yourself !! Answers: 288 18432 288 Assume all the shapes are cubes

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