Tricky integration question

I will be honest, the lecturer went over this in such a weird manner that I have no idea where to even start this question.

An artist decides to fill one of the Fiddler's ferry cooling towers with soup. the tower is 120 m high, its radius at height z is given by

r(z) = sqr root(a^2 +1/4(z - w)^2)

with a = 25 m and w = 90 m

How many litres of soup are needed for this project?

Like I said I don't even know where to start with question so any help is appreciated

The shape of the tower will be circular in horizontal cross-section, so its volume will be formed by rotating the function r(z) about the z-axis.

I'm that clueless at the moment even that doesn't mean a lot. Can you give a but more info? Or even an idea to the technique I can look up to find some notes on

what level are you?

Degree. This is an optional maths module to add up the creds of the degree. So I don't think it's as high as undergrad maths but higher than a level?

have you done volumes of revolution at A Level?

Ah yes the integral with limits is piy^2 dx. So do I just need to integrate the function and use 25 and 90 as my limits or is it slightly more complex?

I think you need cylindrical coords

Ah ok I think I have some notes on that so will try and apply them tomorrow. Thanks for a push in the right direction.

look at my edit too.

I will look at it tomorrow too because I have been doing maths today for nearly 16 hours straight and at the moment I do not remember my 2 times table

Thanks for your help. The lecturer went over it all so weirdly. Ouch 16 hours of maths!I'm surprised you even replied to the thread!!!

No worries

(since 8.30 this morning with hardly any breaks)

goodnight

I think you need cylindrical coords

...

Volume of revolution would cover it, I think.

Hmm, if r(z) is a function, then wouldn't the volume be gotten by integrating the function squared with respect to z, with the limits 0 and 120? Then multiply that by pi and you should get the answer.

That's the volume of revolution method.

Yep, but someone (OP I think) stated up there to use limits of 25 and 90, so I thought I'd chime in to correct that just in case.

Yep, but someone (OP I think) stated up there to use limits of 25 and 90, so I thought I'd chime in to correct that just in case.

Good point - I didn't spot that.