Well start by setting two of the volumes equal to each other.
and find the relationship between w and s. You should be able to form the ratio between them from there.
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 of w, s, t and π (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 ratio w : s : t.
ii: If also w + 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 actually taught how 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.
So I did (1/3)πt^{2}w = πt^{2}s and came out with s = (1/3)w and thus w = s/(1/3). I tried solving (1/3)πt^{2}w = (1/2)*(4/3)πt^{3} for t but failed miserably.
Have I done this right? Also, what significance does this have in finding the ratio?