FCAT CountdownFCAT Countdown

DAY 1 – PART 2DAY 1 – PART 2

VOLUMEVOLUME

Benchmark: Benchmark:

B.2.4.1B.2.4.1

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ObjectivesObjectivesCompute volume of 3D figuresCompute volume of 3D figures

AgendaAgendaReview Volume Review Volume Example ProblemsExample ProblemsPractice Problems for a gradePractice Problems for a grade

Things You Should KnowThings You Should Know

Area of Area of RectangleRectangle = b*h = b*hArea of Area of CircleCircle = = ππrr22

Area of Area of TriangleTriangle = ½ b*h = ½ b*h

Review: VolumeReview: VolumeThis section will cover the five figures This section will cover the five figures

that appear most oftenthat appear most oftenRemember: Area is 2-dimensional Remember: Area is 2-dimensional

and Volume is 3-dimensionaland Volume is 3-dimensionalVolume is the amount of space inside Volume is the amount of space inside

an objectan objectVolume is measured in cubic unitsVolume is measured in cubic units

The Rectangular PrismThe Rectangular Prism Packaging cheese slices Packaging cheese slices

might be a good way to might be a good way to think about finding the think about finding the volume of the rectangular volume of the rectangular prismprism

Ex.1 – How much cheese Ex.1 – How much cheese is contained in the carton is contained in the carton illustrated at right?illustrated at right?

3 in

2 in

5 in

The Rectangular PrismThe Rectangular PrismFirst, we need one slice – the slice is First, we need one slice – the slice is

2 by 3 inches2 by 3 inchesThe area of the slice is 2 * 3 = 6 The area of the slice is 2 * 3 = 6

square inchessquare inches

2 in

3 in

If we stack the cheese 5 in high, we form our rectangular prism.

It’s volume is the area of one slice multiplied by the height!

V = Area of the Base * Height

In this case, 2*3*5 = 30 cubic inches

3 in

2 in

5 in

The CylinderThe CylinderLet’s stack pancakesLet’s stack pancakes

Ex.2 – What is the volume of this stack of pancakes?

The area of one pancake would be: Area of a circle = πr2

= π72

= 49π cm2 Volume = Area of the Base * HeightV = 49π*10= 490π cm3

7 cm

10 cm

The Square PyramidThe Square PyramidThe pyramid is 1/3 of a The pyramid is 1/3 of a

prism.prism.

The volume would be The volume would be V = 1/3*Area of Base* HeightV = 1/3*Area of Base* Height

In this case,In this case,

V = 1/3*10*10*6V = 1/3*10*10*6

= 200 in= 200 in22

10 in

h = 6 in

The ConeThe ConeThe cone is 1/3 the cylinder.The cone is 1/3 the cylinder.

The volume of the cone The volume of the cone would bewould be

V = 1/3*Area of Base*HeightV = 1/3*Area of Base*Height

In this case,In this case,

V = 1/3* V = 1/3* ππ*5*522*12*12

V = 1/3*V = 1/3* π π*25*12*25*12

V = 100V = 100 π π cm cm22

h = 12 cmr = 5 cm

The SphereThe Sphere

• The Volume of the Sphere is The Volume of the Sphere is

4 4

--- --- ππ r r 33

33

Practice ProblemsPractice Problems

Go to Click on the link below to go to Go to Click on the link below to go to the practice problems:the practice problems:

http://stuff4mathclass.com/fcat/crunchtime/volume.html