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CHAPTER 9 Geometry and Measurement Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 9.1Systems of Linear Measurement 9.2Converting Units of Area 9.3More with Perimeter and Area 9.4Volume and Capacity 9.5Angles and Triangles 9.6Square Roots and the Pythagorean Theorem 9.7Weight, Mass, and Temperature 9.8Medical Applications

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OBJECTIVES 9.4 Volume and Capacity Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aFind the volume of a rectangular solid, a cylinder, and a sphere. bConvert from one unit of capacity to another. cSolve applied problems involving volume and capacity.

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9.4 Volume and Capacity a Find the volume of a rectangular solid, a cylinder, and a sphere. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The volume of an object is the number of unit cubes needed to fill it.

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9.4 Volume and Capacity VOLUME OF A RECTANGULAR SOLID Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The volume of a rectangular solid is found by multiplying length by width by height:

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EXAMPLE 9.4 Volume and Capacity a Find the volume of a rectangular solid, a cylinder, and a sphere. 2Volume of a Safe. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. For office security, William purchases a safe with dimensions Find the volume of this rectangular solid.

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9.4 Volume and Capacity a Find the volume of a rectangular solid, a cylinder, and a sphere. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Volumes are described in units such as cubic centimeters (cm 3 ) and cubic inches (in 3 ). Dimensional analysis is an excellent way of determining the correct units for an answer. If measurements of length are added, use a one- dimensional unit of length. If two measurements of length are multiplied, use a two-dimensional unit of area. If three measurements of length are multiplied, use a three-dimensional unit of volume.

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9.4 Volume and Capacity a Find the volume of a rectangular solid, a cylinder, and a sphere. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A rectangular solid is shown. Note that we can think of the volume as the product of the area of the base times the height: where B represents the area of the base.

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9.4 Volume and Capacity a Find the volume of a rectangular solid, a cylinder, and a sphere. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Like rectangular solids, circular cylinders have bases of equal area that lie in parallel planes. The bases of circular cylinders are circular regions.

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9.4 Volume and Capacity VOLUME OF A CIRCULAR CYLINDER Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The volume of a circular cylinder is the product of the area of the base B and the height h:

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EXAMPLE Find the volume of this circular cylinder. Use 3.14 for 9.4 Volume and Capacity a Find the volume of a rectangular solid, a cylinder, and a sphere. 3 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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9.4 Volume and Capacity a Find the volume of a rectangular solid, a cylinder, and a sphere. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A sphere is the three-dimensional counterpart of a circle. It is the set of all points in space that are a given distance (the radius) from a given point (the center). The volume of a sphere depends on its radius.

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9.4 Volume and Capacity VOLUME OF A SPHERE Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The volume of a sphere of radius r is given by

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EXAMPLE The radius of a standard-sized bowling ball is in. Find the volume of a standard-sized bowling ball (disregarding the finger holes). Round to the nearest hundredth of a cubic inch. Use 3.14 for 9.4 Volume and Capacity a Find the volume of a rectangular solid, a cylinder, and a sphere. 4Bowling Ball. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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9.4 Volume and Capacity b Convert from one unit of capacity to another. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To answer a question like How much soda is in the bottle? we need measures of capacity.

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9.4 Volume and Capacity AMERICAN UNITS OF CAPACITY Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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9.4 Volume and Capacity b Convert from one unit of capacity to another. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Fluid ounces, abbreviated fl oz, are often referred to as ounces, or oz.

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EXAMPLE 9.4 Volume and Capacity b Convert from one unit of capacity to another. 5 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Since we are converting from a smaller unit to a larger unit, we multiply by 1 using 1 gal in the numerator and 4 qt in the denominator:

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EXAMPLE 9.4 Volume and Capacity b Convert from one unit of capacity to another. 6 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The box with capacity units does not list how many ounces are in 1 gal. We convert gallons to quarts, quarts to pints, and pints to ounces, using the relationships given in the box.

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EXAMPLE 9.4 Volume and Capacity b Convert from one unit of capacity to another. 6 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Since we are converting from a larger unit to a smaller unit, we use substitution: Thus, 9 gal = 1152 oz.

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9.4 Volume and Capacity b Convert from one unit of capacity to another. Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. One unit of capacity in the metric system is a liter.

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9.4 Volume and Capacity METRIC UNITS OF CAPACITY Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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9.4 Volume and Capacity b Convert from one unit of capacity to another. Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The metric prefixes are also used with liters. The most common is milli-.

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Title 9.4 Volume and Capacity Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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9.4 Volume and Capacity b Convert from one unit of capacity to another. Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A common unit for drug dosage is the milliliter (mL) or the cubic centimeter (cm 3 ). The notation cc is also used for cubic centimeter, especially in medicine. The milliliter and the cubic centimeter represent the same measure of capacity. Volumes for which quarts and gallons are used are expressed in liters. Large volumes are expressed using measures of cubic meters (m 3 ).

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Title 9.4 Volume and Capacity Slide 26Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 9.4 Volume and Capacity b Convert from one unit of capacity to another. 8 Slide 27Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 9.4 Volume and Capacity c Solve applied problems involving volume and capacity. 9 Slide 28Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. At a self-service gas station, 89-octane gasoline sells for 102.6¢ a liter. Estimate the price of 1 gal in dollars. Since 1 liter is about 1 quart and there are 4 quarts in a gallon, the price of a gallon is about 4 times the price of a liter. Thus, 89-octane gasoline sells for about $4.10 a gallon.

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