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# Volume

Prisms, Cylinders, Pyramids, Cones
by

## Susan Bryan

on 5 February 2014

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#### 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
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
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.
88.0 in^3
1,272.3 cm^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