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Math Help - Find surface area to volume ratio

  1. #1
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    Find surface area to volume ratio

    SHOW WORK PLEASE!
    1st find SA, then volume, then the ratio

    1. 2cm x 3cm x 4cm
    2. 6 cm x 8 cmx 10cm
    3. Radius = 4 cm
    4 Radius = .75
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Are those cuboids?

    If so,

    Volume_{cuboid} = l\times b \times h

    Volume_{sphere} = \dfrac43 \pi r^3

    SA_{cuboid} = 2 lb + 2 lh + 2 lh

    SA_{sphere} = 4\pi r^2

    Ratio will be simple then.
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  3. #3
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    I know the formulas, it just doesn't work when I do it or is a decimal.
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Why not?

    a) Volume = lbh = (2)(3)(4) = 24 cm^3

    SA = 2(2)(3) + 2(3)(4) + 2(2)(4) = 12 + 24 + 16 = 52 cm^2

    Ratio = 24 : 52 = 6 : 13
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  5. #5
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    Thanks, I already got that one. It's just the last two with decimals that I can't solve.
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  6. #6
    MHF Contributor Unknown008's Avatar
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    Volume = \dfrac43 \pi (4)^3 = \dfrac43 \pi (64) = \dfrac{256\pi}{3} cm^3

    SA = 4 \pi (4)^2 = 64 \pi\ cm^2

    Ratio = 256/3 : 64 = 4 : 3
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  7. #7
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    Thank you, thank you, thank you!
    But I'm still getting a decimal on the last one D:
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  8. #8
    MHF Contributor Unknown008's Avatar
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    Really? =/

    Volume = \dfrac43 \pi (0.75)^3 = \dfrac{9\pi}{16} cm^3

    SA = 4\pi (0.75)^2 = \dfrac{9\pi}{4} cm^2

    Ratio = 9/16 : 9/4 = 4 : 16 = 1 : 4
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  9. #9
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    Yeah, I know, but I missed class on Thursday/Friday so I wasn't exactly taught how to do it.
    Also, for #2, the ratio 188:225 isn't right, is it?
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  10. #10
    MHF Contributor Unknown008's Avatar
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    Oo

    Volume = (8)(6)(10) = 480 cm^3

    SA = 2(8)(6) + 2(8)(10) + 2(6)(10) = 376 cm^2

    Ratio = 480: 376 = 60 : 47
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