The figure (fig) shows a solid consisting of three parts, a cone, a cylinder and a hemisphere, all of the same base radius.

The first part of the question asks us to find the volume of each part, in terms ofw, s, tandπ (pi):

Volume of cone = (1/3)πt^{2}w

Volume of cylinder = πt^{2}s

Volume of hemisphere = (1/2)*(4/3)πt^{3 }The next part of the question reads:

i: If the volume of each of the three parts is the same, find the ratiow : s : t.

ii: If alsow + s + t = 11, find the total volume in terms of π.

Aaaaaaaand I have no idea, nor am I expected to have an idea -- I was never actuallytaughthow to do this, it was some kind of maniacal challenge set by my teacher to see how I would go about finding an answer.

Any help would be much appreciated. Thanks for your time.