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Math Help - Quick volume problem

  1. #1
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    Lightbulb Quick volume problem

    Im on my last question and i cant figure this out! I have been stuck for a while. Can anyone help me with this really quick?

    You have a ball that is a perfect sphere. You placed it in a tub of water and found that it displaced exactly 280,000 cubic centimetres. However, it was floating on the water, and only 72% of the surface area of the ball was below the water line.

    What was the total volume of the ball, in cubic centimetres? [Round to the nearest whole number]

    thank you for helping
    :]
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by xinfinitex View Post
    Im on my last question and i cant figure this out! I have been stuck for a while. Can anyone help me with this really quick?

    You have a ball that is a perfect sphere. You placed it in a tub of water and found that it displaced exactly 280,000 cubic centimetres. However, it was floating on the water, and only 72% of the surface area of the ball was below the water line.

    What was the total volume of the ball, in cubic centimetres? [Round to the nearest whole number]

    thank you for helping
    :]
    If 72% of the surface area of the ball is submerged then, by proportion,
    \left ( \frac{72}{100} \right ) ^{3/2} \approx 0.611
    or 61.1% of the volume of the ball is submerged.

    Can you do it from here?

    -Dan
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  3. #3
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    I am having trouble figuring out the process to find the solution, so I am unsure of what to do next. I am in 10th grade and I am very new and just learning about volumes. I am very lost.
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  4. #4
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    ok i tried my best and got 346233 cubic centimetres.

    is this correct? if not, what would be correct?
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by xinfinitex View Post
    Im on my last question and i cant figure this out! I have been stuck for a while. Can anyone help me with this really quick?

    You have a ball that is a perfect sphere. You placed it in a tub of water and found that it displaced exactly 280,000 cubic centimetres. However, it was floating on the water, and only 72% of the surface area of the ball was below the water line.

    What was the total volume of the ball, in cubic centimetres? [Round to the nearest whole number]

    thank you for helping
    :]
    Quote Originally Posted by topsquark View Post
    If 72% of the surface area of the ball is submerged then, by proportion,
    \left ( \frac{72}{100} \right ) ^{3/2} \approx 0.611
    or 61.1% of the volume of the ball is submerged.

    Can you do it from here?

    -Dan
    To continue, we know that 61.1% of the volume is submerged, and we know that the volume submerged is 280000 cubic centimeters (since that is the volume of water it displaced. Thus
    \frac{61.1}{100} = \frac{280000~cm^3}{V}

    I get V = 458310~cm^3.

    -Dan
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