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Chapter 13

Chapter 13. Measurement. 13.1 Measurement with Nonstandard Units. The Measurement Process Select an object and an attribute of the object to measure. Select an appropriate unit with which to measure the object.

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Chapter 13

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  1. Chapter 13 Measurement

  2. 13.1 Measurement with Nonstandard Units The Measurement Process • Select an object and an attribute of the object to measure. • Select an appropriate unit with which to measure the object. • Determine the number of units needed to measure the attribute. This may require a measurement device.

  3. Standard Units The English System Length Inch = 1/12th foot Yard = 3 feet Ratios: Inches to feet is 12:1 Feet to yards is 3:1

  4. The English System Area Square foot is the fundamental unit 1 ft 1 ft

  5. The English System Temperature Gabriel Fahrenheit, German instrument maker, inventor of mercury thermometer, in 1714. Freezing point (32°F) and Boiling point (212°F) are used as reference temperatures. Difference in temps is 180°.

  6. Standard Units The Metric System An Ideal System of Units • Portability: Fundamental Unit can be reproduced accurately. • Convertibility: Simple, decimal ratios among units of the same type. • Interrelatedness: Different types of units (length, area, volume) are defined in terms of each other, using simple relationships.

  7. The Metric System Length Fundamental Unit is the meter. 1 meter = 1650763.73 wavelengths of orange-red light in the spectrum of the element krypton 86. Can be reproduced anywhere. Decimal system – multiples and fractions of meter correspond to powers of ten.

  8. The Metric System Area Fundamental unit is square meter.

  9. The Metric System Volume Fundamental unit is liter. 1 mL = 1 cm3 10 cm 10 cm 10 cm

  10. The Metric System Mass Fundamental unit is kilogram. One kilogram is the mass of one liter of water in its densest state. 1 kg is approx. 2.2 pounds

  11. The Metric System Temperature Anders Celsius – 1742 Centigrade the original name of scale. Freezing point (0°C) and Boiling point (100°C) are the reference temperatures. Difference in temps is 100°.

  12. Dimensional Analysis When converting from one system of measurement to another, treat the labels as part of the measurement and include them in the calculations. EX: Convert 17 ft to in.

  13. 13.2 Length and Area Length Distance on a Line • The distance from 0 to 1 is 1 and is called the unit distance. • For all points P and Q, PQ=QP. • If P, Q and R are points on a line and Q is between P and R, then PQ+QR=PR.

  14. Perimeter The perimeter of a polygon is the sum of the lengths of its sides.

  15. Circumference r d

  16. Area Rectangles a b Squares s s

  17. Area Triangles a b

  18. Area Parallelograms h a b

  19. Area Trapezoids b h a

  20. Area Circles r

  21. Pythagorean Theorem c a b

  22. 13.3 Surface Area The surface area of a three-dimensional figure is the total area of its exterior faces. The lateral surface area for solids with bases, is the difference between surface area and the area of the bases.

  23. Formula for Surface Area of Prisms For any right prism with height H, the surface area can be calculated using the formula For a cylinder, the formula is similar, following the same idea as above.

  24. Base 20 20 26 Face 26 20 L 10 20 10

  25. Formula for Surface Area of Pyramids and Cones For a pyramid with slant height L, the surface area can be calculated with the following formula: For a cylinder, the formula is similar, following the same idea as above.

  26. Sphere The surface area of a sphere is found by using the formula below:

  27. 13.4 Volume The volume of a three-dimensional figure is a measure of the amount of space that it occupies. To calculate the volume of a prism, the following formula can be used.

  28. Formula for Volume of Pyramids and Cones For a pyramid with height H, the volume can be calculated with the following formula: For a cone with height H, the volume can be calculated with the same formula.

  29. Sphere The volume of a sphere is found by using the formula below:

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