fcat countdown day 1 – part 2 volumebenchmark:b.2.4.1 use the left and right arrow keys to...
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FCAT CountdownFCAT Countdown
DAY 1 – PART 2DAY 1 – PART 2
VOLUMEVOLUME
Benchmark: Benchmark:
B.2.4.1B.2.4.1
Use the left and right arrow keys to navigate through this presentation.
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
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