1. © 2010 Pearson Education, Inc. All rights reserved Concepts of Measurement Chapter 13

2. Slide 13.5- 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13-5Volume, Mass, and Temperature  Volume of Right Rectangular Prisms  Converting Metric Measures of Volume  Converting English Measures of Volume  Volumes of Prisms and Cylinders  Volumes of Pyramids and Cones  Volume of a Sphere  Mass  Relationships Among Metric Units of Volume, Capacity, and Mass  Temperature

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 3 Volume and Surface Area What is the volume of each figure? What is the surface area of each figure? 9 cubic units 36 square units34 square units

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 4 Volume of Right Rectangular Prisms Right rectangular prism Volume = wh

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 5 Converting Metric Measures of Volume 1 dm 3 = 1000 cm 3

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 6 1 m 3 = 1,000,000 cm 3 1 dm 3 = 0.001 m 3

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 7 Convert each of the following: a.5 m 3 = ______________ cm 3 b.12,300 mm 3 = ______________cm 3 Example 13-23 5,000,000 12.3

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 8 1 liter = 1 dm 3 = 1000 cm 3

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 9 UnitSymbolRelation to Liter kiloliterkL1000 L hectoliterhL100 L dekaliterdaL10 L literL1 L deciliterdL0.1 L centilitercL0.01 L millilitermL0.001 L

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 10 Convert each of the following: a.27 L = _________ mL b.362 mL = _________ L c.3 mL = _________ cm 3 d.3 m 3 = _________ L Example 12-24 27,000 0.362 3 3000

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 11 Converting English Measures of Volume Basic Units of Volume: cubic inch (in. 3 ) cubic foot (ft 3 ) cubic yard (yd 3 ) Volume equivalents: 1 gal = 231 in. 3 1 qt = gal

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 12 Convert each of the following: a.45 yd 3 = _________ ft 3 b.4320 in. 3 = _________ yd 3 Example 13-25

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 13 c.10 gal = _________ ft 3 d.3 ft 3 = _________ yd 3 Example 13-25 (continued)

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 14 Volumes of Prisms and Cylinders Cavalieri’s Principle Two solids each with a base in the same plane have equal volumes if every plane parallel to the bases intersects the solids in cross sections of equal area.

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 15 Find the volume of each figure. 216 cm 3 450 cm 3 250π cm 3 Example 13-26

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 16 Volumes of Pyramids and Cones Right pyramid Volume = where B is the area of the base.

17. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 17 Volumes of Pyramids and Cones Right circular cone Volume =

18. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 18 Find the volume of each of each figure. Example 13-27

19. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 19 Find the volume of the pyramid represented by the net shown. Each triangle is equilateral. Example 13-28

20. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 20 Volume of a Sphere Sphere Volume =

21. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 21 Example 13-29 Find the volume of a sphere whose radius is 6 cm.

22. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 22 Mass: a quantity of matter Weight: a force exerted by gravitational pull Gram: fundamental unit of mass in the metric system Mass

23. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 23 UnitSymbolRelation to Gram metric tonT1,000,000 g kilogramkg1000 g hectogramhg100 g dekagramdag10 g gramg1 g decigramdg0.1 g centigramcg0.01 g milligrammg0.001 g

24. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 24 Convert each of the following: a.34 g = _________ kg b.6836 kg = _________ t 0.034 6.836 Example 13-30

25. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 25 1 cm 3 (1 mL) of water = 1 g 1 dm 3 (1 L) of water = 1 kg Relationships Among Metric Units of Volume, Capacity, and Mass

26. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 26 a.Approximately how many liters of water can it hold? b. What is its mass in kilograms when it is full of water? A waterbed measures 180 cm x 210 cm x 20 cm. Example 13-31 Because 1 L of water has a mass of 1 kg, 756 L of water has a mass of 756 kg, which is 0.756 t.

27. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 27 degree Kelvin: base unit of temperature in the metric system; used only for scientific measurements. The freezing point of water is 273°K. degree Celsius: used for customary temperature measurements in the metric system. Its scale has 100 equal divisions. The freezing point of water is 0°C, and its boiling point is 100°C. Temperature

28. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 28 degree Fahrenheit: used for customary temperature measurements in the English system. Its scale has 180 equal divisions. The freezing point of water is 32°F, and its boiling point is 212°F. Temperature

29. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 29 Comparing Temperatures in Degrees Celsius and Degrees Fahrenheit

30. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.5- 30 Converting between degrees Celsius and degrees Fahrenheit To convert temperatures, use the following formulas: