This is an interesting question.
The side view of the model is on the left. A solid sphere of radius 15 cm is contained inside a pyramid. If the sphere touches all 5 faces of the pyramid, and water is injected into the pyramid such that half of the pyramid is filled. What is the volume of water is injected?
I am stuck! When it says half of the pyramid is filled, does it mean that water level is up to one half of the pyramid's height? I have already calculated that the height is 40 cm.
HINT. You must compute the volume of the frustum (which is $7/8$ of the whole pyramid) and subtract the volume of the spherical cap (the sphere cut at 20 cm from the base).