maths question need help

As.1997

please look at the attachment

-What does an open cylindrical container mean? By open does it mean that it is hollow and it does not have any ends?

(edited 4 years ago)

Screen Shot 2020-02-12 at 20.14.18.png92.7KB

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Reply 1

mqb2766

Original post by As.1997

please look at the attachment

-What does an open cylindrical container mean?

A cylinder with one open and one closed end.

Reply 2

As.1997

Original post by mqb2766

A cylinder with one open and one closed end.

The problem is when you have sheet metal and you make it into a cylindrical container -> shouldn't that be hollow?
BTW if you assume it is hollow and you work accordingly you get the correct answer which is B.

Reply 3

mqb2766

Original post by As.1997

Yes. Its a container so its hollow.

Reply 4

As.1997

Original post by mqb2766

Yes. Its a container so its hollow.

what I meant is shouldn't both ends be open?

Reply 5

mqb2766

Original post by As.1997

what I meant is shouldn't both ends be open?

Not if it contains water?

Reply 6

As.1997

The answer is B. Can you show me how to do it?

Reply 7

aioheuiawe

nvm nvm

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Reply 8

mqb2766

Original post by As.1997

The answer is B. Can you show me how to do it?

There are two parts to it.
* The mass of the water. The mass of the water increases by a factor of 8 (all dimensions are doubled and the mass is a volume)
* The mass of the cylinder. The mass of the cylinder goes up by a factor of 4 (surface area doubles in each dimension, but the thickness is the same).

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Reply 9

mqb2766

Original post by aioheuiawe

The lengths have all been doubled. Therefore the volume (to do with mass) is 2**3 the size. Or 8 times the size. Add the two masses and multiply by 8.

No. The cylinder mass increases by a factor of 4.

Reply 10

As.1997

Original post by mqb2766

No. The cylinder mass increases by a factor of 4.

If the thickness did not stay the same and instead doubled. Would we then consider the metal sheet mass to be a volume and therefore increase by a factor of 8?

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Reply 11

As.1997

For the surface area of the cylinder do you use:
pi*r^2 +2pir?

Since the height and diameter doubles we would do:

pi(2r)^2 + 2pi(2r)= 4pi*r^2 + 4pi*r = 4(pir^2 + pi*r)
Therefore, since 4 is the common factor, the multiplier is 4 and therefore we multiply the original mass of the cylinder (800g) by 4 to get the mass after the diameter and height have doubled?

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Reply 12

mqb2766

Original post by As.1997

If the thickness did not stay the same and instead doubled. Would we then consider the metal sheet mass to be a volume and therefore increase by a factor of 8?

Yes, but is specifically says it stays the same. In this case two of the dimensions double so the volume increases by 4.

Reply 13

As.1997

Original post by mqb2766

Yes, but is specifically says it stays the same. In this case two of the dimensions double so the volume increases by 4.

I am still puzzled by the metal sheet. If it is open ended ie one side is closed and one side is open, then for the side with the closed part how do we take into consideration the change in size for that?

(If this doesn’t make sense - I’m simply asking doesn’t the bottom of the cylinder which is closed increase by a factor of 4? If so how do we take this into consideration)

Reply 14

mqb2766

Original post by As.1997

The actual shape doesn't matter. Two dimensions are doubled and one stays the same. The two shapes are simliar in the "doubled" dimensions hence the area increases by 4 and so does the volume as the other dimension stays the same.

The bottom of the shape is treated in exactly the same way as the side, and they both can be lumped together, as the lumped shape will be similar to the larger lumped shape.

Edit - Just seen your post 12. They do not want you to do this (too long / complex). The simpler answer is just the ratio of dimsensions for similar shapes, and interpret the area and volume in terms of products of these ratios. Questions like these are not unusual.

(edited 4 years ago)

Reply 15

As.1997

Original post by mqb2766

I understood most of your explanation. The bit I need some clarification with is “they can both be lumped together as the lumped shape will be similar to the larger lumped shape” —> what does this mean?

Reply 16

mqb2766

Original post by As.1997

Just that you can consider a single (lumped) shape which is the side (rectangle) + bottom (circle). Which has two dimensions doubled, hence the new shape is similar in two dimensions and the area is 4 times the original "lumped shape". They don't have to be considered separately.

Reply 17

As.1997

Original post by mqb2766

Perfect I get u thank u

Reply 18

As.1997

Original post by As.1997

Perfect I get u thank u

Would I be right in thinking of it like this:

— imagine I melted the shape (cylinder) and made it into a cube shape with only the height and weight doubling —> this would result in a cube with a volume that is 4 times bigger

Is this a good analogy or is there a flaw in this idea of thinking?

(I believe it is pretty much the same as what you said above)

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Reply 19

mqb2766

Original post by As.1997

height and ***width***? As far as I understand what you're saying, then yes.
If you had a unit cube (volume of 1), but doubled the length and width. The dimensions are (2*2*1) so volume 4 (similar length - width face). If you doubled all dimensions, which is similar to the original shape, then volume 8.