Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

Volume

Prisms, Cylinders, Pyramids, Cones
by

Susan Bryan

on 5 February 2014

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of Volume

VOLUME
Volume: Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid.
Its units are always "cubic", that is, the number of identical cubes that fit inside the figure.
For Example
l
A= l x w
A= 8cm x 2cm
A= 16 cm
2
V= lwh
or
V = Bh
3 cm
3cm
3cm
V= s
V= 3cm x 3cm x 3cm
V= 27 cm
3
3
10 cm
6cm
4cm
V= lwh
V= 10cm x 4cm x 6cm
V= 240cm
3
V= Volume
l = length
w= width
h= height
B = base area
V= lwh
V= 2cm x 2cm x 8cm
V= 32 cm
3
Rectangular Pyramid
4cm
4cm
7cm
V= 1/3 lwh
V= 1/3 (7cm x 4cm x 4cm)
V= 37.3 cm
3
Cylinder
10m
6m
V= Bh B = πr
V=πr h
V= 3.14 x 3cm x 10cm
V= 282.6cm
2
2
3
Cone
V= 1/3 πr h
2
4km
7.5km
4km
8.5km
?
Pythagorean Theorem
A + B = C
2
2
2
C - A = B
8.5km - 4km = B
72.25 - 16 = 56.25
√ 56.25= 7.5
7.5= B
2
2
2
2
2
2
V= 1/3 πr h
V= 1/3 ( π x 4km x 7.5km)
V= 125.7 km
2
2
3
SPHERE
V= 4/3 πr
3
12m
V= 4/3 πr
V= 4/3 π x 12
V= 7238.2km
3
3
3
V= 7238.2km / 2
V= 3619.1km
2
2
Relations Between Shapes.
A right pyramid is related to a right prism.
A right cone and a cylinder.
A sphere and a Cylinder
8cm
2cm
8cm
2cm
2cm
Volume of Composite Objects.
To find the volume of this composite object, you will have to find the volume of the hemispheres first.
V= 4/3 πr
V= 4/3 (3.14 x 1)
V= 4.186'
2
3
V= πr h
V= 3.14 x 1 x 6
V= 18.84'
3
2
V= 23.026'
3
Then find the volume of the Cylinder
Then add them together.
First find the volume of the rectangular prism
3cm
V= lwh
V= 5cm x 5cm x 7cm
V= 175 cm
3
Then find the volume of the cone.
V= 1/3πr h
V= 1/3 (3.14 x 2.25cm x 5cm
V= 11.775cm
2
3
5cm
Now subtract the volume of the cone from the volume of the rectangular prism.
V= 175cm - 11.775 cm
V= 163.225 cm
3
3
3
A Mathematician says: Pi r squared
A Baker replies: Pi r round not squared, cake is squared.
A cube is a "box" where height, width and depth are all the same. We can compare volumes of figures when the "boxes" are the same size.
1 cm
1 cm
1 cm
This box is 1 cm on each side. We call it "one cubic centimeter". We write it as 1 cm^3.
What if the base of the prism is NOT a square or rectangle?

Find the area of the base and multiply it by the height of the prism.
B = lw which is the area of the base
Or:

Base area is 2 cm x 2 cm = 4 cm^2

Base Area x Height = Volume

4 cm^2 x 8 cm = 32 cm^3
4 cm
10 cm
height of triangle is 5 cm
Area of Triangle: 1/2 bh
=1/2 (4)(5)
= 10 cm^2

Volume of Triangular Prism
= Bh
= (10 cm^2)(10 cm)
= 100 cm^3
Slant Height
The distance from the
vertex to the circumference
of the base.
2
2
2
2
Ask questions.
Do the practice problems.
Prisms and Cylinders (7-5)
Pyramids and Cones (7-6)

2
STOP
Do the practice problems for 7-5, Volume of Prisms and Cylinders
After you complete the mastery check for 7-5, return to here to learn about Volume of Pyramids and Cones.
Do this mini-lab at home.
Answers:
88.0 in^3
1,272.3 cm^3
Answer: 228 in^3
What did you learn about the volume of a pyramid?
What is the volume of this pyramid?
The volume of a pyramid is 1/3 the volume of the prism with the same base and height.
V = 1/3 Bh
Answer: 6.7 yd^3
Answer:
pi 4 * 7.5
2
3
= 125.67 km

3

The volume of a cone is 1/3 the volume of the cylinder with the same base and height.
Full transcript