# Math Help - Quick volume problem

1. ## 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
:]

2. Originally Posted by xinfinitex
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

3. 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.

4. ok i tried my best and got 346233 cubic centimetres.

is this correct? if not, what would be correct?

5. Originally Posted by xinfinitex
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
:]
Originally Posted by topsquark
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