Average Volume of Half a Sphere

[Icheb]

A sphere is submerged half way in water and pulled out at a constant speed. Now I have to find out the average volume of the part of the sphere that is under water.

The volume formula would be $$4/3 \pi r^3$$, now the part of the sphere that is under water at first would be $$2/3 \pi r^3$$.

Initially I thought I could assume the sphere to be a cube and then calculate the volume of the cube under water. Half of that volume would be the result then since the velocity is constant. However I'm not sure if that approximation is alright?


Edit: Never mind, found it! :)

 

[berkeman]

Glad you found it. Did you use integration to get the answer, or is there a simpler way?