SURFACE
AREA
&
VOLUME
What is Surface Area?
Surface Area is the area of each
surface of the figure
You will have to find the area of
each side of the figure and add
them together
NOTE: all measurements will be
squared!!! (since it’s area)
Surface Area Example
13 in.
12 in.
11 in.
2 rectangles:
A= L x W
A= 13 x 11
A= 143 in.2
2 rectangles:
A= L x W
A= 12 x 11
A= 132 in.2
There are 6
rectangles in this
prism. Find the
area of all & add.
2 rectangles:
A= L x W
A= 13 x 12
A= 156 in.2
• 143 + 143 + 132 + 132 + 156 + 156 = 862 in.2
Practice Problem 2
• Find the surface area of the triangular
prism shown to the right.
• Find the area of each shape and add.
Area of the
triangle #1
A = ½ bh
A = ½ (12)(16)
A = 96 cm2
Area of the
triangle #2
A = ½ bh
A = ½ (12)(16)
A = 96 cm2
Area of the
rectangle #1
A=LxW
A = 20 (10)
A = 200 cm2
Area of the
rectangle #2
A=LxW
A = 16 (10)
A = 160 cm2
SA = 96 + 96 + 200 + 160 + 120
SA = 672 cm2
Area of the
rectangle #3
A=LxW
A = 12 (10)
A = 120 cm2
Practice Problem 3
• Find the surface area of the
cylinder.
• There are 2 circles and 2
rectangles in a cylinder
2 circles:
A = r2
A = 62
A = 36
A = 113.04
2 “rectangles”:
A = rh
A = (6)(18)
A = 108
A = 339.12
Surface Area =
113.04 + 113.04 + 339.12 + 339.12 = 904.32 in.2
What is Volume?
Volume is the measure of the
capacity of a container.
It is the measure of how
much a container of a
particular shape will hold liquids, dry substances, etc.
Cubic Units
Volume is measured in cubic units.
Use cubes to fill a rectangular prism
such as a box.
One Cubic Unit
1 unit
(length)
1 unit
(height)
A unit might be
measured in
inches, feet,
centimeters, etc.
1 unit
(width)
Note: All measurements will be cubed! 14in.3
How many cubic units is
this rectangle?
What did you
find?
Yes, it is 8
cubic units!
How about this one?
Remember…
there are some
cubes you can’t
see!
Yes! There
are 12 cubic
units!
What’s the formula?
The formula for finding the volume
of a rectangle is ….
Volume = L x W x H
This means we take the length
times the width, then multiply
that by the height.
Let’s try it!
L=3
H=3
W=2
3 x 3 x 2 = 18
cubic units
The Volume Of A Triangular Prism.
Consider the triangular prism below:
The formula for the volume of a
triangular prism is :
V=½bhl
5cm
B= base h = height l = length
8cm
5cm
Calculate the volume:
Volume = ½ b h l
V = ½ (5)(5)(8)
V = 100 cm3
The Volume Of A Cylinder.
Consider the cylinder below:
The formula for the
volume of a cylinder is:
6cm
V = r 2h
r = radius
h = height.
Calculate the volume:
4cm
V= r 2xh
V=x2x2x6
V = 75.36 cm3
What Goes In The Box ? 2
Calculate the volume of the shapes below:
(1)
(2)
14cm
4m
5m
2813.4cm3 16cm
3m
30m3
(3)
8m
6cm
12cm
288cm3