Cylinder problem

~Bitzchick~ · Joined: 05 Aug 2007 Posts: 18

Hi all

Here's a problem i've been trying to solve but cannot get the same answer as
the answer given

An open cylinderical container made from sheet metal of uniform thickness,
has a mass of 800g. When completely filled with water, the total mass is
15.6kg

What would be the total mass of the cylinderical container full of water
made from the same sheet metal (of same thickness) but with double the the
diameter and double the height ?

I make it 124.8kg

but the answer 'should' be 121.6kg

Can anyone help?

TIA

sheri

--
Life may not be the party we hoped for, but whilst we are here we might as
well dance

Archived from group: uk>education>maths

David W. Cantrell · Joined: 05 Aug 2007 Posts: 5

"~Bitzchick~" wrote:
> Hi all
>
> Here's a problem i've been trying to solve but cannot get the same answer
> as the answer given
>
> An open cylinderical container made from sheet metal of uniform
> thickness, has a mass of 800g. When completely filled with water, the
> total mass is 15.6kg
>
> What would be the total mass of the cylinderical container full of water
> made from the same sheet metal (of same thickness) but with double the
> the diameter and double the height ?
>
> I make it 124.8kg

That's presumably because you used 15.6kg * 2^3. But that is incorrect
because it treats the sheet metal as if its thickness also doubled.

The answer you mentioned below is correct. I hope you will now be able to
get it yourself.

David

> but the answer 'should' be 121.6kg
>
> Can anyone help?
>
> TIA
>
> sheri

~Bitzchick~ · Joined: 05 Aug 2007 Posts: 18

David W. Cantrell wrote:
> "~Bitzchick~" wrote:
>> Hi all
>>
>> Here's a problem i've been trying to solve but cannot get the same
>> answer as the answer given
>>
>> An open cylinderical container made from sheet metal of uniform
>> thickness, has a mass of 800g. When completely filled with water, the
>> total mass is 15.6kg
>>
>> What would be the total mass of the cylinderical container full of
>> water made from the same sheet metal (of same thickness) but with
>> double the the diameter and double the height ?
>>
>> I make it 124.8kg
>
> That's presumably because you used 15.6kg * 2^3. But that is incorrect
> because it treats the sheet metal as if its thickness also doubled.
>
> The answer you mentioned below is correct. I hope you will now be
> able to get it yourself.
>
Thanks for your response but...
I'm afraid not. Here is my arguable logic...

Density of material = mass/volumeof material

so volume = mass/density. If density remains constant then volume is
proportional to mass. So if the volume of the larger cylinder is 8 times
bigger than the volume of the smaller cylinder, (I proved the maths) then
the mass of the larger cylinder must be 8 times bigger. I can't see how the
thickness of the material comes into it?

sheri

~Bitzchick~ · Joined: 05 Aug 2007 Posts: 18

David W. Cantrell wrote:
> "~Bitzchick~" wrote:
>> Hi all
>>
>> Here's a problem i've been trying to solve but cannot get the same
>> answer as the answer given
>>
>> An open cylinderical container made from sheet metal of uniform
>> thickness, has a mass of 800g. When completely filled with water, the
>> total mass is 15.6kg
>>
>> What would be the total mass of the cylinderical container full of
>> water made from the same sheet metal (of same thickness) but with
>> double the the diameter and double the height ?
>>
>> I make it 124.8kg
>
> That's presumably because you used 15.6kg * 2^3. But that is incorrect
> because it treats the sheet metal as if its thickness also doubled.
>
> The answer you mentioned below is correct. I hope you will now be
> able to get it yourself.
>

Oh I think I've got it

taking the sheet metal as having a length and a width and a thickness

the volume of the metal would be length x width x thickness

but if the thickness stays the same and you double the width (diameter) and
the length (the height) BUT keep the thickness the same. You are only
multiplying the length x width, ie 2 x 2 = 4
so if density = mass/volume, so if mass is proportional to volume OF METAL,

then metal mass of large cylinder is 4 x bigger than metal mass of small
cylinder

So 0.8kg x 4 = 3.2 kg
therefore new total volume = 118.4 + 3.2 = 121.6kg

Goodness me!

Thanks David Surprised

))

sheri

Chris Holford · Joined: 18 Oct 2007 Posts: 1

In article , ~Bitzchick~
writes
snip
>Density of material = mass/volumeof material
Snip

-no need to calculate density;

The volume, and hence the mass of water will increase by a factor of 2x2x2

The AREA of metal, and hence the mass will increase by a factor of 2x2
(for metal of the same thickness)
--
Chris Holford

~Bitzchick~ · Joined: 05 Aug 2007 Posts: 18

Chris Holford wrote:
> In article ,
> ~Bitzchick~ writes
> snip
>> Density of material = mass/volumeof material
> Snip
>
> -no need to calculate density;
>
> The volume, and hence the mass of water will increase by a factor of
> 2x2x2
>
> The AREA of metal, and hence the mass will increase by a factor of 2x2
> (for metal of the same thickness)

Yes yes yes. I'm so bloody annoyed to have not considered the metal itself,
I could kick myself! I thought the question meant that the cylinder was an
idealised hypothetical solid object and for the sake of rhe question, the
thickness would stay constant to ease the maths!!

I'm so angry with myself with seeing the question as an exercise and not
real life, as it were.

I shall crawl into a hole and weep now Sad

(

I wish I was as clever as you lot

sheri

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