Thread: Algebra (Volume, Ratios)

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)πt²w

Volume of cylinder = πt²s

Volume of hemisphere = (1/2)*(4/3)πt³

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.

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.

So I did (1/3)πt²w = πt²s and came out with s = (1/3)w and thus w = s/(1/3). I tried solving (1/3)πt²w = (1/2)*(4/3)πt³ for t but failed miserably.

Have I done this right? Also, what significance does this have in finding the ratio?

Bump. Anyone?

Originally Posted by ibdutt

So how did you go from having (1/3)w = s = (2/3)t to having the ratio (6:2:3)?

And also, where did "k" come from?

Thanks heaps. One final question to clarify my understanding: do we divide by 2 to make each fraction (1/X), (1/Y), etc? (i.e to turn (2/3) into (1/3) we must divide it by 2 and thus all the others by 2)

Yes we divide the fractions by a suitable number so that we have 1 in the numerator of each fraction, in this case we divide by 2.

Thanks heaps.