Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 8.2 Length, Area and Volume.

Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 8.2

Length, Area and Volume


What You Will Learn

How to determine which unit of length is appropriateHow to determine which unit of area is appropriateCalculate areasHow to determine which unit of volume is appropriateCalculate volumes

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Length

The meter (metre) is used to measure things that we normally measure in yards and feet. Kilometer is used to measure things that we normally measure in miles.Centimeters and millimeters are used to measure what we normally measure in inches.

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Length

Centimeters and millimeters

Inches

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Example 1: Choosing an Appropriate Unit of LengthDetermine which metric unit of length you would use to express the following.a) The height of the statueof Babe, Paul Bunion’sBlue Ox.

Meters

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Example 1: Choosing an Appropriate Unit of Lengthb) The length of your nose

Millimeters or centimeters

c) The length of a fleaMillimeters

d) The height of the Empire State Building

Meters

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Example 1: Choosing an Appropriate Unit of Lengthe) The diameter of a half-dollar

Millimeters or centimeters

f) The distance between Dallas, Texas, and Chicago, Illinois.

Kilometers

g) The diameter of a round wastepaper basket

Centimeters8.2-7


Example 1: Choosing an Appropriate Unit of Lengthh) The diameter of a pencil

Millimeters

f) Your waist sizeCentimeters

j) Your heightMeters or centimeters

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AreaAreas are always expressed in square units: square centimeters, square kilometers, or square meters.

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AreaSquare centimeter replaces square inches.Square meter replaces square foot or square yard.Square kilometer replaces square mile.One square kilometer is about 4/10 square mile.

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AreaA hectare is a square unit 100 meters on each side (a square hectometer) and is symbolized ha.A hectare is about 2.5 acres.One square mile of land contains about 260 hectares.

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Example 2: Choosing an Appropriate Unit of AreaDetermine which metric unit of area you would use to measure the area of the following.a) Yellow StoneNational Park

Square kilometersor hectares

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Example 2: Choosing an Appropriate Unit of Areab) The top of a kitchen table

Square meters

c) The floor of a classroomSquare meters

d) A person’s property with an average-sized lot

Square meters or hectares

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Example 2: Choosing an Appropriate Unit of Areae) A newspaper page

Square centimeters

f) A baseball fieldHectares or square meters

g) An ice-skating rinkSquare meters

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Example 2: Choosing an Appropriate Unit of Areah) A dime

Square millimeters orsquare Centimeters

f) A lens in eyeglassesSquare Centimeters

j) A dollar billSquare Centimeters

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Example 4: Table TopFind the area of a rectangular table top if its length is 1.5 m and its width is 1.1 m.

Solution Use Area = length ×

width A = l × w A = 1.5 m × 1.1 m = 1.65 m2

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Example 5: A Circular TableA circular table has a diameter of about 76 cm. Find the surface area of the table.

SolutionUse A = πr2

π is approximately 3.14r = ½ diameter

A ≈ 3.14(38 cm)2

A ≈ 4534.16 cm2

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Volume

When a figure has three dimensions: length, width and height, the volume can be found.The volume of an item can be considered the space occupied by the item.Volume of liquids can be expressed in terms of liters.

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Volume

A liter is a little larger than a quart.Liters are used in place of pints, quarts, and gallons.A liter can be divided into 100 equal parts, each part is called a milliliter.Milliliters are used to express the volume of very small amounts of liquid.Drug doses are often expressed in ml.

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Volume

The kiloliter is used to represent the volume of large amounts of liquid.Cubic meters are used to express the volume of large amounts of solid and gaseous material.

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VolumeThe liquid in a liter container will fit exactly in a cubic decimeter.1l = 1000 ml and 1 dm3 = 1000 cm3

1l = 1 dm3 and 1 ml = 1 cm3

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Volume

1 m3 = 1 kl

1 dm3 = 1 l

1 cm3 = 1 ml

Volume in LitersVolume in Cubic Units

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Example 6: Choosing an Appropriate Unit of VolumeDetermine which metric unit of volume you would use to measure the volume of the following.a) The water in CraterLake (the deepestlake in the UnitedStates)

Kiloliters

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Example 6: Choosing an Appropriate Unit of Volumeb) A carton of milk

Liters

c) A truckload of topsoilCubic meters

d) A liquid drug dosageMilliliters

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Example 6: Choosing an Appropriate Unit of Volumee) Sand in a paper cup

Cubic centimeters

f) A dimeCubic millimeters

g) Water in a drinking glassMillimeters

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Example 6: Choosing an Appropriate Unit of Volumeh) Water in a swimming pool

Kiloliters or liters or cubic meters

f) The storage area of a sports utility vehicle with the back seats folded down or removed

Cubic metersj) Concrete used to lay the

foundation for a basementCubic meters

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Example 7: Swimming Pool VolumeA swimming pool is 18 m long and 9 m wide, and it has a uniform depth of 3 m. Find (a) the volume of the pool in cubic meters and (b) the volume of water in the pool in kiloliters.

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Example 7: Swimming Pool Volume18 m long, 9 m wide, and depth of 3 m

Solutiona) Use V = l × w × h

= 18 m × 9 m × 3 m = 486 m3

b) 1 m3 = 1 kl, the pool will hold 486 kl

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Example 10: A Hot-Water HeaterA hot-water heater, in the shape of a right circular cylinder, has a radius of50 cm and a height of148 cm. What is the capacity, in liters, of the hot-water heater?

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Example 10: A Hot-Water Heaterradius of 50 cm and a height of 148 cm

SolutionUse V = πr2h

π is approximately 3.14We need to express the answer in liters so we will express the measurements in meters. The answer will be in cubic meters which can be converted to liters.50 cm = 0.5m, 148 cm = 1.48 m

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Example 10: A Hot-Water HeaterSolutionradius = 0.5 m and height = 1.48 m

Use V = πr2h V ≈ 3.14(0.5)2(1.48) V ≈ 3.14(0.25)(1.48) V ≈ 1.1618 m3

Convert to liters: 1 m3 = 1000 l1.1618 m3 = 1.1618 × 1000 = 1161.8 lThe hot-water heater’s capacity is about 1161.8 l.

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Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 8.2 Length, Area and Volume.

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Transcript of Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 8.2 Length, Area and Volume.