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Math Help - Surface Area basic

  1. #1
    Member
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    Mar 2008
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    Angry Surface Area basic

    hai...

    i have confusing in order to get the ans for the following attached problem. i already attached the my ans.
    Surface Area basic-q.jpgSurface Area basic-.jpg

    the correct ans from book: 659.82 cm^2
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  2. #2
    Newbie driegert's Avatar
    Joined
    Feb 2010
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    Kingston, Ontario
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    Hey,

    So the surface area of a cylinder is:

    SA_{cyl} = 2\pi r^2 + 2\pi rh

    Since we are taking off the top of the cylinder we can change it to:

    SA_{cyl} = \pi r^2 + 2\pi rh

    Next we need the surface area for a cone, minus the area of the base of the cone.

    SA_{cone} = \pi rs + 2\pi r^2

    Again, we don't need the base of the cone, so we get:

    SA_{cone} = \pi rs

    This formula requires a value 's' which is the diagonal length (straight dotted line in your picture). We get this from Pythagoras.

    s^2 = h^2 + r^2 \Rightarrow s = \sqrt{12^2 + 5^2} = 13

    There we are! We have everything we need. So, the surface area of our modified cylinder is:

    SA_{mod} = SA_{cyl} + SA_{cone} =  (\pi r^2 + 2\pi rh) + (\pi rs)
    SA_{mod} = (\pi 5^2 + 2\pi(5)(12)) + (\pi (5)(13)) = 660 cm^2

    At least, that's what I get. Hope it helps!
    --
    Dave
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  3. #3
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    if i not mistaken the surface area of cone is SA_{cone} = \pi rs + \pi r^2
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