Volume of the solid revolution

I’ve been doing a C4 edexcel past paper from 2014, and i’m stuck on part b) of the question. I’m not sure if I need to know this for the new OCR maths syllabus. Many Thanks

That topic is not part of A Level maths anymore. That's the risk with trying old spec papers - it can be hard to know if a question is relevant to new spec.

Thanks. Also, is this question part of the new syllabus? I’m stuck with part b), and part c)

Yes it is. You've probably done similar (maybe a bit easier) questions before in your textbook? Please post your answer to a) and any working/thoughts for b) and I can help you.

This is my answer for part a). I haven’t got anything for part b). I didn’t know where to start.

If I asked you what the maximum value is of $2\sin \theta - 4\cos \theta$ would you know that? I'm just checking if you know how to do the more standard questions before tackling this harder question.

Do differentiate and make equal to zero? Or is it something to do with the sin and cos graphs?

What topic does this come under? I have the CGP book for OCR, will it be in there? @Sir Cumference

It will be somewhere within trigonometry. Look for the part that teaches Rsin/cos forms and it will be part of that.

It will be somewhere within trigonometry. Look for the part that teaches Rsin/cos forms and it will be part of that.

Is this it? This is the example I found in the CGP book.

In the CGP book it doesn’t have any practice question on this, and I don’t have my OCR textbook on me. Could you send me a link to some practice questions please. Thanks

@Anonymous_4657 here are the answers to that worksheet:

https://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Worksheets-Notes/Solomon/C3%20Trigonometry%20F%20-%20Answers.pdf

How do you know the max is 25? Where did the x-16.3 = 90 come from? You probably think I’m being really stupid.

Firstly you're not stupid. This forum is for questions from any level so never be embarrassed about asking for help.

You're considering the function

$y=25\sin(x-16.3)$

If you imagine the graph, this is the standard sine function translated by 16.3 to the right and stretched vertically by 25. Here's what it looks like:

https://www.desmos.com/calculator/taukf47klw

You can see that the maximum is 25. This is because the maximum of sin(x) is 1 and it's been stretched by 25. There are infinitely many maximums as you can see but the question asks for the smallest x value that gives a maximum. So basically you're just solving the equation

$25\sin(x-16.3) = 25$

i.e

$\sin(x-16.3) = 1$

This is where x - 16.3 = 90 (to get the smallest value of x).