Surface Area and Volume Powerpoint 1

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    GeometryFormulas:

    Surface Area

    & Volume

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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 rectangle

    is 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 f ind the surface area of a pr ism

    by adding up the areas of all the surfaces