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7/28/2019 ArtySurface Area & Volume
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Geometry Formulas:
Surface Area
& Volume
ARTYCLASS -10B
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A formula is just a set of instructions.
It tells you exactly what to do!
All you have to do is look at the
picture and identify the parts.
Substitute numbers for the variables
and do the math. Thats it!
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Lets start in the beginning
Before you can do surface area or volume,
you have to know the following formulas.
Rectangle A = lwTriangle A = bh
Circle A = r
C = d
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You can tell the
base and height
of a triangle by
finding the
right angle:
TRIANGLES
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CIRCLES
You must know the difference
between RADIUS and DIAMETER.
r
d
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Lets start with a rectangular prism.
Surface area can be done using the formula
SA = 2 lw + 2 wl + 2 lw OR
Either method will gve you the same answer.
you can find the area
for each surface and
add them up.
Volume of a rectangular prism is V = lwh
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Example:
7 cm
4 cm
8 cm
Front/back 2(8)(4) = 64
Left/right 2(4)(7) = 56
Top/bottom 2(8)(7) = 112
Add them up!
SA = 232 cm
V = lwh
V = 8(4)(7)
V = 224 cm
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To find the surface
area of a triangular
prism you need to beable to imagine that
you can take the
prism apart like so:
Notice there are TWO congruent triangles
and THREE rectangles. The rectanglesmay or may not all be the same.
Find each area, then add.
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Example:
8mm
9mm
6 mm 6mm
Find the AREA of each SURFACE
1. Top or bottom triangle:
A = bh
A = (6)(6)
A = 18
2. The two dark sides are the same.
A = lw
A = 6(9)
A = 54
3. The back rectangleis different
A = lw
A = 8(9)
A = 72
ADD THEM ALL UP!
18 + 18 + 54 + 54 + 72
SA = 216 mm
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SURFACE AREA of a CYLINDER.
You can see that
the surface is
made up of two
circles and arectangle.
The length of the rectangle is the same as
the circumference of the circle!
Imagine that
you can open up
a cylinder like
so:
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EXAMPLE: Round to the nearest TENTH.
Top or bottom circle
A = r
A = (3.1)
A = (9.61)
A = 30.2
Rectangle
C = length
C = d
C = (6.2)
C = 19.5
Now the area
A = lw
A = 19.5(12)
A = 234
Now add:
30.2 + 30.2 + 234 =
SA = 294.4 in
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There is also a formula to find surface area of a cylinder.
Some people find this way easier:
SA = 2rh + 2r
SA = 2(3.1)(12) + 2(3.1)
SA = 2 (37.2) + 2(9.61)
SA = (74.4) + (19.2)
SA = 233.7 + 60.4
SA = 294.1 in
The answers are REALLY close, but not exactly the same.
Thats because we rounded in the problem.
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Find the radius and height of the cylinder.
Then Plug and Chug
Just plug in the numbers then do the math.
Remember the order of operations and youre
ready to go.
The formula tells you what to do!!!!
2rh + 2r means multiply 2()(r)(h) + 2()(r)(r)
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Volume of Prisms or Cylinders
You already know how to find the volume of a
rectangular prism: V = lwh
The new formulas you need are:
Triangular Prism V = ( bh)(H)
h = the height of the triangle and
H = the height of the cylinder
Cylinder V = (r)(H)
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Volume of a Triangular Prism
We used this drawing for our surface
area example. Now we will find the
volume.
V = ( bh)(H)
V = (6)(6)(9)
V = 162 mm
This is a
right
triangle, so
the sides are
also the base
and height.
Height of
the prism
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Try one:
Can you see thetriangular bases?
V = ( bh)(H)
V = ()(12)(8)(18)
V = 864 cm
Notice the prism is on
its side. 18 cm is the
HEIGHT of the prism.
Picture if you turned itupward and you can
see why its called
height.
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V = (r)(H)
V = ()(3.1)(12)
V = ()(3.1)(3.1)(12)
V = 396.3 in
Volume of a Cylinder
We used this drawing for oursurface area example. Now we will
find the volume.
optionalstep!
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Try one:
10 m
d = 8 m
V = (r)(H)
V = ()(4)(10)
V = ()(16)(10)
V = 502.7 mSince d = 8,
then r = 4
r = 4 = 4(4) = 16
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Here are the formulas you will need to know:
A = lw SA = 2rh + 2r
A = bh V = ( bh)(H)
A = r V = (r)(H)
C = d
and how to find the surface area of a prismby adding up the areas of all the surfaces