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volumes of revolution

so, for b, I've chosen to revolves the curve around the y axis, with the top curves volume being measures from 12 to 7, and the bottom one 8 to 7. I've subtracted the volume of the bottom curve from the top. however this doesnt give me the right answer.
(edited 4 years ago)
Screenshot 2020-02-14 at 10.06.25.png370.4KB
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You've rotated around the wrong axis. The question makes it clear that you need to rotate around the x-axis.
Original post by dextrous63
You've rotated around the wrong axis. The question makes it clear that you need to rotate around the x-axis.


ok, I see that but shouldnt it give me the right/same answer?
Original post by FurtherMaths2020
ok, I see that but shouldnt it give me the right/same answer?

No. It will create an entirely different shape (ie a ring, and not some kind of weird eggshell thingy!!)
Original post by dextrous63
No. It will create an entirely different shape (ie a ring, and not some kind of weird eggshell thingy!!)

:biggrin: touche
Original post by FurtherMaths2020
ok, I see that but shouldnt it give me the right/same answer?

Definetly not.

think about the volume your creating as you pull the 2D cross section around the axis.
You might find it useful to develop your Geogebra/Autograph skills to draw 3D shapes. Good fun (in a strange sort of way). Also highly useful for drawing parametric curves, amongst other things.
Original post by dextrous63
You might find it useful to develop your Geogebra/Autograph skills to draw 3D shapes. Good fun (in a strange sort of way). Also highly useful for drawing parametric curves, amongst other things.

I totally see it now - I hadn't had my morning coffee and was feeling a little sluggish.
Original post by dextrous63
You might find it useful to develop your Geogebra/Autograph skills to draw 3D shapes. Good fun (in a strange sort of way). Also highly useful for drawing parametric curves, amongst other things.


Original post by mnot
Definetly not.

think about the volume your creating as you pull the 2D cross section around the axis.


ok, so back to this question. I got the volume as 704.355, but it's in mm, and the density is in g/cm.

so, I have to divide mm by 10, to get cm? (this is the step im unsure about)

to get

density x volume = mass

to get the right answer, do I need to convert the equation for mass in in terms of meters and KG?
(edited 4 years ago)
Original post by FurtherMaths2020
ok, so back to this question. I got the volume as 704.355, but it's in mm, and the density is in g/cm.

so, I have to divide mm by 10, to get cm? (this is the step im unsure about)

to get

density x volume = mass


Density is grams / cm^3 but since 1cm = 10mm it means that density here is grams / (10^3 mm^3) ... meaning you need to divide your current density by 10^3 to get the one for grams / mm^3, and hence use this one to obtain the mass in grams.
Original post by RDKGames
Density is grams / cm^3 but since 1cm = 10mm it means that density here is grams / (10^3 mm^3) ... meaning you need to divide your current density by 10^3 to get the one for grams / mm^3, and hence use this one to obtain the mass in grams.


is density always: grams / cm^3?
Original post by FurtherMaths2020
is density always: grams / cm^3?


Of course not. It can be kg / m^3.

The units range from one context to another, but the dimensions of density are always the same: it's some mass divided by some volume.
Original post by RDKGames
Of course not. It can be kg / m^3.

The units range from one context to another, but the dimensions of density are always the same: it's some mass divided by some volume.

so, my volume is in millimetres and needs to be not just cm but cm^3, like the density? V(CM^3) x D(g/CM^3) = VD(g) = M(g) ?
Original post by FurtherMaths2020
so, my volume is in millimetres and needs to be not just cm but cm^3, like the density? V(CM^3) x D(g/CM^3) = VD(g) = M(g) ?


You can either convert your volume answer from part (b) into cm^3,

OR you can convert your density into being g / cm^3


Either way, multiply volume by the density and you will end up with the same answer.
Original post by RDKGames
You can either convert your volume into cm^3,

OR you can convert your density into being g / cm^3


Either way, multiply volume by the density and you will end up with the same answer.


so, dividing volume by 10 gives me cm, but I want cm^3, so I convert by (10)^3 ?
Original post by FurtherMaths2020
so, dividing volume by 10 gives me cm, but I want cm^3, so I convert by (10)^3 ?


Just think back to GCSE

1cm = 10 mm

So cube both sides and you get

1cm^3 = 10^3 mm^3


Hence if your volume is in cm^3, then thats the same as it being 10^3 lots of the mm^3 measurement.

Hence for volume in mm^3 you need to multiply your volume in cm^3 by 10^3

If going the other way, i.e. you have volume in mm^3 but want the volume in cm^3, then you need to divide your volume by 10^3.
(edited 4 years ago)
Original post by FurtherMaths2020
ok, so back to this question. I got the volume as 704.355, but it's in mm, and the density is in g/cm.

so, I have to divide mm by 10, to get cm? (this is the step im unsure about)

to get

density x volume = mass

to get the right answer, do I need to convert the equation for mass in in terms of meters and KG?


Volume is mm^3 presumably. and no, you have to remeber to cube the factor of 10 so:
10mm = 1cm
therefore its 1000mm^3 = 1cm^3

yes density x volume = mass
Original post by RDKGames
Just think back to GCSE

1cm = 10 mm

So cube both sides and you get

1cm^3 = 10^3 mm^3


Hence if your volume is in cm^3, then thats the same as it being 10^3 lots of the mm^3 measurement.

Hence for volume in mm^3 you need to multiply your volume in cm^3 by 10^3

If going the other way, i.e. you have volume in mm^3 but want the volume in cm^3, then you need to divide your volume by 10^3.

PRSOM
Original post by RDKGames


If going the other way, i.e. you have volume in mm^3 but want the volume in cm^3, then you need to divide your volume by 10^3.


isn't that what we just did now? I divided volume by 10^3 and multiplied it by density, to get mass.
Original post by FurtherMaths2020
isn't that what we just did now? I divided volume by 10^3 and multiplied it by density, to get mass.


i don't know if that's what you did, it doesn't sound very precise when you're jumbling lingo and saying things like

"dividing volume by 10 gives me cm"

and then

"convert by 10^3"

These phrases hold no meaning to me as a mathematician.

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