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[SOLVED] Surface Area of ball floating in water

dwsmith

Well-known member
Feb 1, 2012
1,673
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

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
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

Well-known member
Feb 1, 2012
1,673
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

Administrator
Staff member
Feb 24, 2012
13,775
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.