Maths.......

[Bingbing10]

Hey guys , so i have a maths GCSE exam tomorrow ( which i am revising for now) and i am doing this question but just dont have a clue how to work it out.  :mellow: so this forum is full of some very smart people and was wondering if anyone could aid me.

thanks

 

[Demonicreature]

Hey guys , so i have a maths GCSE exam tomorrow ( which i am revising for now) and i am doing this question but just dont have a clue how to work it out.  :mellow: so this forum is full of some very smart people and was wondering if anyone could aid me.

thanks

 

I'm in secondary 2 and I have not learned that... I think its the end of the year or something..

[Bingbing10]

I'm in secondary 2 and I have not learned that... I think its the end of the year or something..

 

wait sorry im not catching on 

[KamiKatze]

i guess the sphere that's immeresd has a infinite height?

 

Calculate the volume without the sphere. 

 

let me think, I'll edit it later.

 

Edit: the volume of the cylinder without the sphere is 16x² * Pi * h

 

When you put the sphere in, it takes up a volume of 9 x² * Pi * h

 

So you can only fit a volume of 7 x² * Pi in 1*h

 

for the additionaly 9 x² * Pi, you will need another 9/7 h. So all in all, the cylinder will have a height of 16/7 h

 

that all is valid, assuming that the submersed sphere has a infinite height.

 

never mind, i calculated with anotehr cylinder, not a sphere. -.-

[brownninja97]

i never understood those kinda questions back when i did gcse last year, i did luck out and it was a 4 mark question instead of 6 as it normally is

[TNortham112]

Hey guys , so i have a maths GCSE exam tomorrow ( which i am revising for now) and i am doing this question but just dont have a clue how to work it out.  :mellow: so this forum is full of some very smart people and was wondering if anyone could aid me.

thanks

 

Woooooo I got Maths GCSE exam tomorrow as well, good luck!!

[Bingbing10]

i guess the sphere that's immeresd has a infinite height?

 

Calculate the volume without the sphere. 

 

let me think, I'll edit it later.

well you are not allowed to use a calculator either and ive got the volumes in terms of x just dont know the rest

[Bingbing10]

Woooooo I got Maths GCSE exam tomorrow as well, good luck!!

im from bristol as well 

[Ciccioo]

calculate V, the volume of the sphere

pretend that V is the volume of a cylinder with the same base as the given cylinder

calculate the height of that cilinder, that should be your answer

[Cacao]

Ok.. So we know that the water will rise as much as the volume of the sphere. The volume of the sphere is 4/3 π 27x^3 cm^3. Now we add that volume to the original volume of the cylinder before the sphere is immersed, which is π 16x^2 h. So the total final volume is (4/3 π 27x^3) + (π 16x^2 h).

 

Now we know you calculate the volume of a cylinder by doing:

 

V = π r^2 h

 

So from here we know that h = V/(π 16x^2) so h2 = (4/3 π 27x^3) + (π 16x^2 h) / (π 16x^2)

 

Work that out and you should have h.

[Bagmup]

My cats breath smells like cat food..

[TNortham112]

im from bristol as well 

 

Cool:P

[NUFCThomas]

i've got my maths gcse exam tomorrow as well, good luck , doing mine a year early

[xox]

Working... Haven't done maths in a year, so it may take 5 mins

 

 

Oh god, got this:

 

xincrease = 135.1x

 

Yeah, I think it's safe to say that I can't do maths anymore. Dem Logarithms mess with me.

 

area of Sphere = πr³

Area of Cylinder = πr²xh

 

This means that the volume in the sphere is 84.8x cm³ and the volume of the Cylinder is 50.3hx cm³

 

height increase = 50.3hx + 84.8x   (Heights cancel out)

general increase = 135.1x

 

I remember being so much better at this

 

 

EDIT:Just out of interest, what did the markscheme say?

EDIT 2:Need to revise for AS Physics 2 tomorrow, bye

Edited June 8, 2014 by tomlambert01

[Cacao]

im from bristol as well 

Pss follow your topic

 

Also, this should be in off topic... 

[Bingbing10]

Pss follow your topic

 

Also, this should be in off topic... 

im trying to follow your working but failing 

[xox]

im trying to follow your working but failing 

You are not trying to work out h here, just increase in terms of x.

 

It is impossible to find h, there is a value missing.

[Cacao]

im trying to follow your working but failing 

Well I hope it's correct, but pretty much what I did was add the volume of the sphere to the original volume of the water, that way we have the final volume of the water right?

 

So you can calculate the volume of that water by doing V = π r^2 h. If you look in that equation we know the value of V (original volume of water + volume of sphere), we know the value of Pi obviously and we know the radius of the the cylinder. So we can use it to find the height. So if you move it around a bit you get that the final height (h) = V / π r^2.

 

It's kind of hard to explain via text Anyway I'm not even 100% sure it's correct, that's how I would do it though.

 

EDIT: Just go with @tomlambert01 I think I overcomplicated things

[wjdobie]

Wow I've just completed AS Maths and this seems awful! Which Exam Board is it?

I think I've got the answer, The difference In volume = the volume of the sphere itself, and as the volume of the sphere in terms of x = 3/4π27x^3, I think that may be the answer, I'll share my working page in a sec, but thats what I think it is...

I dont know if there is something else I need to do, let me think some more...

EDIT: It might be that you use the volume of the sphere, then treat that equation (3/4π27x^) as the volume of a Cylinder, which gives you "3/4π27x^ ÷ π16x^2 which (Should) cancel down to 1.28125x.

I think i have heavily overthought this, But hey, 

Final Guess: Try sticking with 20.25x^3 / 16x^2 instead of simplifying further, I really am doubting my whole solution now

[Bingbing10]

Working... Haven't done maths in a year, so it may take 5 mins

 

 

Oh god, got this:

 

xincrease = 135.1x

 

Yeah, I think it's safe to say that I can't do maths anymore. Dem Logarithms mess with me.

 

area of Sphere = πr³

Area of Cylinder = πr²xh

 

This means that the volume in the sphere is 84.8x cm³ and the volume of the Cylinder is 50.3hx cm³

 

height increase = 50.3hx + 84.8x   (Heights cancel out)

general increase = 135.1x

 

I remember being so much better at this

 

 

EDIT:Just out of interest, what did the markscheme say?

EDIT 2:Need to revise for AS Physics 2 tomorrow, bye

i cannot find the mark scheme

[MrTomnus]

Wow I've just completed AS Maths and this seems awful! Which Exam Board is it?

I think I've got the answer, The difference In volume = the volume of the sphere itself, and as the volume of the sphere in terms of x = 3/4π27x^3, I think that may be the answer, I'll share my working page in a sec, but thats what I think it is...

I dont know if there is something else I need to do, let me think some more...

I'm in my last year of A level and this has me stumped. The way you should do it would be to work out both volumes, add them to make the new volume, then equate that to the volume of a cylinder to get the new height, then subtract h to get the difference. However in my working, the heights cancelled... And x is 0.

 

[Bingbing10]

I'm in my last year of A level and this has me stumped. The way you should do it would be to work out both volumes, add them to make the new volume, then equate that to the volume of a cylinder to get the new height, then subtract h to get the difference. However in my working, the heights cancelled... And x is 0.

 

IMG_20140608_153027.jpg

i can get up to the stage you're at but i cant do anything else and i cannot find the mark scheme

 

 

aslo how come when you do 4/3 pi 3x^3 you then get 4/3 pi 27x^3 and not just 27 ? ( since havent you already cubed it ?

[Bingbing10]

i guess the sphere that's immeresd has a infinite height?

 

Calculate the volume without the sphere. 

 

let me think, I'll edit it later.

 

Edit: the volume of the cylinder without the sphere is 16x² * Pi * h

 

When you put the sphere in, it takes up a volume of 9 x² * Pi * h

 

So you can only fit a volume of 7 x² * Pi in 1*h

 

for the additionaly 9 x² * Pi, you will need another 9/7 h. So all in all, the cylinder will have a height of 16/7 h

 

that all is valid, assuming that the submersed sphere has a infinite height.

 

never mind, i calculated with anotehr cylinder, not a sphere. -.-

 

 

Ok.. So we know that the water will rise as much as the volume of the sphere. The volume of the sphere is 4/3 π 27x^3 cm^3. Now we add that volume to the original volume of the cylinder before the sphere is immersed, which is π 16x^2 h. So the total final volume is (4/3 π 27x^3) + (π 16x^2 h).

 

Now we know you calculate the volume of a cylinder by doing:

 

V = π r^2 h

 

So from here we know that h = V/(π 16x^2) so h2 = (4/3 π 27x^3) + (π 16x^2 h) / (π 16x^2)

 

Work that out and you should have h.

 

 

Working... Haven't done maths in a year, so it may take 5 mins

 

 

Oh god, got this:

 

xincrease = 135.1x

 

Yeah, I think it's safe to say that I can't do maths anymore. Dem Logarithms mess with me.

 

area of Sphere = πr³

Area of Cylinder = πr²xh

 

This means that the volume in the sphere is 84.8x cm³ and the volume of the Cylinder is 50.3hx cm³

 

height increase = 50.3hx + 84.8x   (Heights cancel out)

general increase = 135.1x

 

I remember being so much better at this

 

 

EDIT:Just out of interest, what did the markscheme say?

EDIT 2:Need to revise for AS Physics 2 tomorrow, bye

dont know if you can help me out with this one

 

[smjpl]

The increase is directly caused by the sphere.

 

The sphere is calculated as 4/3*pi*(3*x)^3  = 4/3*pi*27*x^3

 

So we need to rewrite this in the form of a cylinder:

 

4/3*27 = 36 = 16*2.25

 

=> pi*36*x^3 can be rewritten as:

 

pi*16*x^2*(2.25x) = area*height

 

The increase in height due to the sphere is 2.25x

 

I am not sure if this is the correct answer. Just my guess.

[Bingbing10]

The increase is directly caused by the sphere.

 

The sphere is calculated as 4/3*pi*(3*x)^3  = 4/3*pi*27*x^3

 

So we need to rewrite this in the form of a cylinder:

 

4/3*27 = 36 = 16*2.25

 

=> pi*36*x^3 can be rewritten as:

 

pi*16*x^2*(2.25x) = area*height

 

The increase in height due to the cylinder is 2.25x

it wants it in fraction form