[SOLVED] Surface Area of ball floating in water

[dwsmith]

Using calculus, how would I derive a formula for the exposed surface area of a ball floating in water?

For such a formula to be a good candidate, it would have to consider oscillations of the water and placid water.

The surface area of a sphere is \(A = 4\pi r^2\).

 

[HallsofIvy]

Using calculus, how would I derive a formula for the exposed surface area of a ball floating in water?

For such a formula to be a good candidate, it would have to consider oscillations of the water and placid water.

The surface area of a sphere is \(A = 4\pi r^2\).

That will depend upon the density of the sphere. And if the surface of the water oscillates, the ball will oscillate with it but I don't think that will change the amount of surface area above the water.

 

[dwsmith]

That will depend upon the density of the sphere. And if the surface of the water oscillates, the ball will oscillate with it but I don't think that will change the amount of surface area above the water.

Without knowing density, how could this be done?

If we think of waves, there are waves that entirely overtake objects floating in the water even if it is just for a moment. Therefore, there can be times that the ball is fully submerged. So the the amount above can be anywhere from the max (placid) to 0 rogue waves.

 

[MarkFL]

If I were to use the calculus, I would treat the problem as a surface of rotation, at least to find a formula for the surface of a spherical cap.