You are Here: Home >< Maths

# C4 Volumes of Revolution watch

1. Okay, so I've been able to do most of it, there are 3 questions I'm stuck on, so I'd really appreciate some worked solutions. They are as follows:

7) SOLVED

8) SOLVED

10) SOLVED

Apologies for the potentially rubbish latex, I've been attempting to use it by using the article thing, so some of it may be totally wrong
2. Post some working, or at least an attempt, or your thoughts. These can't be the first volumes of revolution you have done. Most people that are able will be happy to help, but not many are going to give you worked solutions, particularly as it is against forum policy.
3. I'll give hints for 7.

The formula for volumes of revolution is pi*S(y^2)dx between a and b, the lower and upper values of x.

A circle with centre (2, 0) and radius 2, has the equation..?
So y = ?
The distance from the centre is 2, so the upper and lower values for x are..?
4. (Original post by AnonyMatt)
I'll give hints for 7.

The formula for volumes of revolution is pi*S(y^2)dx between a and b, the lower and upper values of x.

A circle with centre (2, 0) and radius 2, has the equation..?
So y = ?
The distance from the centre is 2, so the upper and lower values for x are..?
Yeah I thought that, so is the equation not

The limits would be 4 and 0, but then rearranging to give

But that isn't an option
5. (Original post by xXxBaby-BooxXx)
Yeah I thought that, so is the equation not

The limits would be 4 and 0, but then rearranging to give [latex] y^2 = 4 - (x-2)^2

But that isn't an option
Correct, but if you expand out (x-2)^2 you get x^2 - 4x + 4
4 - x^2 + 4x - 4
Lo and behold, the constans cancel, giving 4x - x^2.

When in doubt, expand them out!
6. And because I'm feeling generous, question 8:

y = secx
y^2 = sec^2x
Integrating gives tanx
Applying the limits gives root3 - 0 = root3

Multiplying by pi, gives pi*root3. I hope this is an option. *scrolls up*
It is.

Hopefully you have this down to an art now.
7. (Original post by ghostwalker)
Post some working, or at least an attempt, or your thoughts. These can't be the first volumes of revolution you have done. Most people that are able will be happy to help, but not many are going to give you worked solutions, particularly as it is against forum policy.
Question 8,

so

This gives a standard integral of 1/k tan k x

With k being 1

so that makes it tan x, which is not a solution for any of the options when subbing in the limits.

Question 10 I just have no idea where to even begin.
8. (Original post by AnonyMatt)
Correct, but if you expand out (x-2)^2 you get x^2 - 4x + 4
4 - x^2 + 4x - 4
Lo and behold, the constans cancel, giving 4x - x^2.

When in doubt, expand them out!
Yeah I did that and got +8

Stupid double negatives, always catches me out!!

By the way, possibly the best catchphrase ever
9. (Original post by xXxBaby-BooxXx)
Question 8,

so

This gives a standard integral of 1/k tan k x

With k being 1

so that makes it tan x, which is not a solution for any of the options when subbing in the limits.
Beg to differ. What's tan(pi/3) - tan(0)? And then multiply by pi.
10. (Original post by AnonyMatt)
And because I'm feeling generous, question 8:

y = secx
y^2 = sec^2x
Integrating gives tanx
Applying the limits gives root3 - 0 = root3

Multiplying by pi, gives pi*root3. I hope this is an option. *scrolls up*
It is.

Hopefully you have this down to an art now.

I should be shot for the amount of stupid mistakes I make. I always get so close to the answer as well
11. (Original post by ghostwalker)
Beg to differ. What's tan(pi/3) - tan(0)? And then multiply by pi.
Mmm hmm I know

Calculator wasn't in radians, and I struggle working with radians in my head. I hate the things!
12. Question 10 is a toughie.

You have to recognise that a sphere is the result of a circle, with it's centre on the y axis, revolving around the x axis.

Try to visualise this. We have a circle, say, with centre (0,0) and the given radius is 2. A 'plane' (now that we're working in 2d, this is just a line) intersects the circle. Suppose this line is x = 1. This is because we know that the line is 1cm from the centre. Think about what will happen to the circle as it revolves around the x axis, and what the shape will look like if we remove all below the line x = 1. With a bit of thought, this is not a 'cap' as the question suggests. With a bit more thought, the only 'line' that will give a cap upon revolving around the x axis, is y = 1. Well, y = -1 too, but you don't like negative numbers, right?

So, what we're saying is, we're revolving the circle x^2 + y^2 = 4, and we've placed a line at |y| = 1. Notice how the line, infinite in length, has become a plane upon revolving around the x axis.
However, we only want the 'cap'. So this is the entire circle, minus everything to the left of y = 1 (or to the right of y = -1). This gives us our limits. They are 1 and 2, or -2 and -1. If you can't see why, quote and ask.
Now you can solve the question as normal.
13. (Original post by AnonyMatt)
Okay, I got

Please tell me this is right!?
14. (Original post by xXxBaby-BooxXx)
Okay, I got

Please tell me this is right!?
Mmhmm.
15. (Original post by AnonyMatt)
Mmhmm.
YAY

Although re-reading your post I realised I did it the long way, by finding out the whole area of the circle and then taking away the area that's not the "cap"

Why do I make so much work for myself?

And +rep for you, not that it's worth anything at all

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 7, 2010
The home of Results and Clearing

### 2,743

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. SAE Institute
Animation, Audio, Film, Games, Music, Business, Web Further education
Thu, 16 Aug '18
2. Bournemouth University
Fri, 17 Aug '18
3. University of Bolton
Fri, 17 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams