SA and Volume of Solids May 03, 2010
Surface Area and Volume of Solids
Objective
Find the surface
area and volume
of solids
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SA and Volume of Solids May 03, 2010
What is a Psolid?
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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SA and Volume of Solids May 03, 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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SA and Volume of Solids May 03, 2010
Examples of Prisms
Prism with two circular bases (Cylinder)
Prism with two pentagonal bases and
5 rectangular faces
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SA and Volume of Solids May 03, 2010
So, how do we find the
surface area of a prism?
First, "unfold" the prism so that all the surfaces lie flat. This is called making a "net".
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SA and Volume of Solids May 03, 2010
Solid
Net
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SA and Volume of Solids May 03, 2010
Now, find the area of all the
separate pieces and add them
together.
Area of a prism = Area of 2 bases + Area of all faces
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SA and Volume of Solids May 03, 2010
Solid
Net
6 in.
Label the "net"
and find the
surface area
15 in.
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SA and Volume of Solids May 03, 2010
6 in.
15 in.
Solid
Net
6 in.
A = 36 A = 90
6 in.
6 in.
15 in.
6 in.
6 in.
A = 90
6 in.
6 in.
15 in.
A = 90
6 in.
6 in.
15 in.
15 in.
6 in.
6 in.
A = 36 6 in.
A = 90
6 in.
6 in.
15 in.
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SA and Volume of Solids May 03, 2010
6 in.
15 in.
A = 90
6 in.
A = 36 6 in.
6 in.
15 in.
6 in.
A = 90
6 in.
6 in.
Surface Area
15 in.
A = 90
6 in.
15 in.
6 in.
6 in.
A = 36 6 in.
6 in.
A = 90
6 in.
SA = 36 + 36 + 90 + 90 + 90 + 90
= 72 + 360
= 432 square inches
6 in.
15 in.
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SA and Volume of Solids lin
y
C
May 03, 2010
r
e
d
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SA and Volume of Solids May 03, 2010
To find the surface area of the cylinder, we need to find the area of a the two circles and one rectangle.
SA = Area of 2 circles + Area of rectangle
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SA and Volume of Solids May 03, 2010
. r
h
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SA and Volume of Solids May 03, 2010
. r
r
Circumference of circle (2 r)
h
h
h
Circumference of circle (2 r)
r
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SA and Volume of Solids May 03, 2010
SA of Cylinder:
r
2 (Area of Circle) + Area of Rectangle
Circumference of circle (2 r)
h
h
Circumference of circle (2 r)
2 ( r 2 ) + C(h)
2 ( r 2 ) + 2 r (h)
2 r (r + h)
r
Therefore, the formula can be simplified to:
SA = 2 r (r + h)
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SA and Volume of Solids May 03, 2010
Try One!!
h = 12 in.
r = 3 in.
r
h
1. Start with the formula
SA = 2 r (r + h)
2. Plug in the numbers
SA = 2 (3) (3 + 12)
= 2 (3.14)(3)(3+12)
= 2 (3.14)(3)(15)
= 282.6 square inches
(Use = 3.14)
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SA and Volume of Solids May 03, 2010
What is volume?
- .
.
.
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SA and Volume of Solids May 03, 2010
.
, ( ).
, .
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SA and Volume of Solids May 03, 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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SA and Volume of Solids May 03, 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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SA and Volume of Solids May 03, 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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SA and Volume of Solids May 03, 2010
Let's Try Another One!
Step 1:
A of base = 1/2 b h
= 1/2 (3)(4)
= 6
7 in.
Step 2:
4 in.
3 in.
V = A h
base
= 6 7
= 42 cubic inches
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SA and Volume of Solids May 03, 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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SA and Volume of Solids May 03, 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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SA and Volume of Solids May 03, 2010
HOMEWORK
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