Volumes of Prisms May 05, 2010
Volumes of Prisms
Objective
Find the volumes
of prisms.
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Volumes of Prisms May 05, 2010
What is a solid?
P
y
m
s
ra
i
m
r
A solid is a
id
P
three‐dimensional
Cy
lin
shape.
e
de
n
o
r
C
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Volumes of Prisms May 05, 2010
Prism
A prism is a solid that has two congruent bases.
Congruent means "same size and same shape".
The base of a prism can be any shape.
This prism has two square bases and four rectangular faces.
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Volumes of Prisms May 05, 2010
Examples of Prisms
Prism with two circular bases (Cylinder)
Prism with two pentagonal bases and
5 rectangular faces
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Volumes of Prisms May 05, 2010
What is volume?
- .
.
.
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Volumes of Prisms May 05, 2010
.
, ( ).
, .
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Volumes of Prisms May 05, 2010
So, how many shapes are
stacked on top of each other?
This is determined by the height of the prism.
h
Height = # of squares stacked on top of each other
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Volumes of Prisms May 05, 2010
Therefore, the volume of a
prism can be expressed by
the formula:
Volume = Area of base (height of prism)
Simplified, it looks like this:
V = A h
base
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Volumes of Prisms May 05, 2010
Let's Try One!
Find the volume of this prism:
Step 1: Find the area of the base
A = 5 5
= 25
8 cm
5 cm
Step 2: Plug numbers into the formula
V = A h
base
= 25 8
= 200 cubic centimeters
3
(also written 200 cm )
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Volumes of Prisms May 05, 2010
Let's Try Another One!
Step 1:
A of base = 1/2 b h
= 1/2 (3)(4)
= 6
4 in
.
Step 2:
.
7 in
.
3 in
V = A h
base
= 6 7
= 42 cubic inches
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Volumes of Prisms May 05, 2010
A cylinder is just like any other prism.
It is made up of many circles stacked on top of
each other.
The volume of a cylinder is:
V = A h
base
= (Area of circle) h
2
= r h
Simplified:
2
V = r h
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Volumes of Prisms May 05, 2010
Try one!
Use the formula:
3
V = r h
2
7
= 3.14 (32)(7)
= 3.14 (9) (7)
= 197.82 cubic units
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Volumes of Prisms May 05, 2010
HOMEWORK
page 627 (1 ­ 11)
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