Volume of Cylinders, Prisms, Cones, and Pyramids

Volume of...

Cylinders

Prisms

Cones

Pyramids

Max Edwards- Sterling Heights

Jacquline Orjada- Sterling Heights

Area-

Amount of space an object covers

Base-

Bottom part of an object.

Height-

Distance from the -> base to the top.

Radius- From the center of the circle to the circumference.

Circumference- Length around the entire circle. To find the circumference take pi and multiply it by the radius times two.

60cm^3

and Pyramids

Real World Use

Behind Door Number 3

At Greenfield Village you make a candle; to pay you need to figure out the volume.

Volume of the cylinder can be used to find the amount of wax that made the candle.

Clues…

Pointy top

Volume = 1/3 * Area of Base * Height

Any shape can be its base

Real World Use

Industries can use the volume formula for prisms to find the volume of simple objects, like juice boxes.

Behind Door Number 2

Clues…

No flat sides

Volume = 1/3 π * Radius^2 * Height

One circle base

GLCE G.SR.08.06

G-geometry ................

SR-spacial resoning and geometric modeling

08- taught in 8th grade..

06- 6th thing suppose to be taught..................

Grade

Level

Content

Expectations

Behind Door Number 1

Clues…

It has parallel bases

Volume = Area of Base * Height

Can be used to see a rainbow

GLCE G.SR.08.06

Volume fomulas for:

• Cylinders
• Prisms
• Cones
• Pyramids

Apply to solve problems

Volume-

Amount and object can hold within a certain boundary.

3D shape- A solid object that has a volume and a height.

VOCABULARY

Resources

Bonus Door

Resources

http://math.about.com/od/formulas/ss/surfaceareavol_2.htm

http://math.about.com/od/formulas/ss/surfaceareavol_3.htm

http://www.staff.vu.edu.au/mcaonline/units/measure/meavol.html

http://www.onlinemathlearning.com/volume-formula.html

http://dictionary.reference.com/browse/cylinder

http://dictionary.reference.com/browse/Prism

http://dictionary.reference.com/browse/Pyramid

Behind Door Number 4

Practice?

http://www.google.com/imgres?hl=en&biw=1024&bih=620&gbv=2&tbm=isch&tbnid=v7Z6XgHEKI_toM:&imgrefurl=http://www.bibleplaces.com/dashur.htm&docid=k9894I37i3CptM&imgurl=http://www.bibleplaces.com/images/Red_Pyramid_with_camel,_tb_n110400.jpg&w=400&h=300&ei=o7o9T6DjJ4mSgwfvsuivCA&zoom=1&iact=hc&vpx=425&vpy=291&dur=1159&hovh=194&hovw=259&tx=124&ty=91&sig=117124217122663471308&page=1&tbnh=120&tbnw=161&start=0&ndsp=15&ved=0CGkQrQMwBw

http://www.gaston.k12.nc.us/schools/cramerton/faculty/kllasky/Course%20Outline%20and%20Syllabus/Textbook/Ch%2012/Text%2012.6%20Volume%20Cylinders.pdf

http://s1.hubimg.com/u/2162296_f520.jpg

http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p020.shtml

Clues…

Circular top and bottom

Volume = π * r^2 * height

Has no flat sides

Cylinder: V=4710cm^3 r=10cm

4710≈3.14*102*h

4710≈314*h

h=15

Prism: V=200cm^3 h=8cm

200= 8ab

200/8=8ab/8

ab=25cm^2

Cylinder

Any Questions ???

Definition:

3D shape

2 parallel circle planes

Connected by 2 parallel lines

Area of a circular base = π*radius2

Volume=π*radius2*

height

Let’s Play Guess Who ???

Prism

Definition:

3D shape

Same parallel base

Parallelogram sides

Volume= area of base*height

h

V= area of base*height

V=ab*h

ab= 6cm2 h=12cm

V=6*12

V=72cm3

3cm

4cm

Height= 12cm

Area of base= 6cm^2

Clues...

volume of a pyramid

area of base= 12cm^2

height= 5

Cone

Definition:

3D shape

Circle base

Pyramid on top

Volume=1/3π*

radius2*height

Cylinders and Prisms!

Need the area of the base and height.

Two same shape parallel planes.

Planes are connected by parallel lines.

Height meets at 90º angle.

Cones and Pyramids!

Taking 1/3 of the area of the base

Need the height

Meet at a common vertex

Pyramid

Definition:

3D shape

Polygonal base

Triangular sides connected at a vertex.

Volume= 1/3*area of base*height

3cm

V=1/3*area of base*height

V=1/3*ab*h

ab=9cm2 h=4cm

V=1/3*9*4

V=3*4

V=12cm3

3cm

Height = 4 cm

Area of Base = 9 cm ^2