Easier way to do it?

[Devaraja]

Hi, I need help with this task my daughter got in school.
She needs to get how much aquarium full of water weight.
Aquarim size is 25cm x 15cm x 20cm, glass thickness is 1cm.
I have two questions, is my calculation correct and is there an easier way to do it?
Here is my calculation:
Aquarium volume:
25*20*15= 7500cm³
Glass volume:
(25*15*1*2)+(20*15*1*2)=1350cm³ *1000000=0.00135m³
Water volume:
7500cm³-1350cm³=6150cm³*1000000=0.00615m³
Glass Weight:
(Glass density = 2500kg/m³)
2500*0.00135=3.375kg
Water weight:
(Water density = 1000kg/m³)
1000*0.00615=6.15kg
Aquarium weight:
6.15+3.375=9.525kg

 

[Otis]

Hi Devaraja. I haven't checked all your calculations, yet, but I can see your method generally, and it seems okay. However, it looks like you've forgotten about the glass bottom of the aquarium.

(25*15*1*2)+(20*15*1*2)=1350cm³ *1000000=0.00135m³

Based on your calculation above, you're treating 15cm as the height of the walls.

Please confirm the following.

(1) The outside dimensions are 20cm long by 25cm wide by 15cm high

(2) We're assuming that the aquarium is filled to the very brim (not realistic).

?

 

[Steven G]

Usually 25cm x 15cm x 20cm (at least to me) means that the length is 25cm, the width is 15 cm and the height is 20cm. This makes sense so that the front viewing will be the largest.

Is the volume you were given (25 x 15 x 20) the inside volume or the outer volume? This will make a difference.

In my opinion, you should help your daughter do the problem both ways or at least talk about the 2nd way so that she learns that these type of problems are not always so clear and can be interpreted in more than one way.

 

[Deleted member 4993]

Hi, I need help with this task my daughter got in school.
She needs to get how much aquarium full of water weight.
Aquarim size is 25cm x 15cm x 20cm, glass thickness is 1cm.
I have two questions, is my calculation correct and is there an easier way to do it?
Here is my calculation:
Aquarium volume:
25*20*15= 7500cm³
Glass volume:
(25*15*1*2)+(20*15*1*2)=1350cm³ *1000000=0.00135m³
Water volume:
7500cm³-1350cm³=6150cm³*1000000=0.00615m³
Glass Weight:
(Glass density = 2500kg/m³)
2500*0.00135=3.375kg
Water weight:
(Water density = 1000kg/m³)
1000*0.00615=6.15kg
Aquarium weight:
6.15+3.375=9.525kg

I have not checked actual calculations. I am assuming that the aquarium has top + bottom and 4 walls. Draw a sketch (with glass thickness) and I assume the dimensions given are the external dimensions of the aquarium. I am getting:

Volume of aquarium = 7500 cc

volume of water = 5382 cc

Volume of glass = 2118 cc

If the aquarium is open-top - then of course number will have to change.

 

[Otis]

… [having the height greater than the width] makes sense so that the front viewing will be the largest …

Indeed. However, storage aquariums are not necessarily designed for viewing.

Also, we may very well need to do the exercise twice, if the assignment doesn't specify whether the given dimensions are inside or outside. A quick check shows that manufacturers differ, in choosing which set of dimensions to report on their labels.

I'm waiting to hear what the OP thinks, about my assumptions in post 2 …

?

 

[Otis]

… I am assuming that the aquarium has top [too] …

A glass top? (I can't recall seeing an example of that.)

Oh, I just had another thought. Are aquariums built such that each of the four walls rests on top of the bottom glass (versus having the walls surround the glass bottom)?

Such an exercise statement ought to be accompanied by an illustration with detailed measurements labeled. Otherwise, we may need to do the exercise four different ways, heh.

?

 

[Deleted member 4993]

A glass top? (I can't recall seeing an example of that.)?

Go to a commercial aquarium where you can walk on top of shark (and you will be glad that the aquarium had glass-top!)

But I thought the simplest problem of this type would be to consider a hollow glass-brick. This is where we need a sketch.......

 

[Otis]

… a commercial aquarium where you can walk on top of shark …

Considering the glass is only 1cm thick, I'll let you stand on that aquarium's lid, Subbo.

By the way, what kind of shark could swim within such an aquarium (given the water volumes that we're considering)?



PS: I'd edited post #6, while you were replying (in case you missed that added commentary).

 

[Deleted member 4993]

A glass top? (I can't recall seeing an example of that.)

Oh, I just had another thought. Are aquariums built such that each of the four walls rests on top of the bottom glass (versus having the walls surround the glass bottom)?

Such an exercise statement ought to be accompanied by an illustration with detailed measurements labeled. Otherwise, we may need to do the exercise four different ways, heh.

?

Anyway - that is why I had suggested that a sketch needs to be drawn - so that the structure is fully defined.

 

[Otis]

… a sketch needs to be drawn …

Good idea. Let the student design their own aquarium, by choosing their own numbers for any required measurements that have not been provided. That way, the exercise is done only once (and maybe the instructor learns something).

?

 

[Devaraja]

Usually 25cm x 15cm x 20cm (at least to me) means that the length is 25cm, the width is 15 cm and the height is 20cm. This makes sense so that the front viewing will be the largest.

Is the volume you were given (25 x 15 x 20) the inside volume or the outer volume? This will make a difference.

In my opinion, you should help your daughter do the problem both ways or at least talk about the 2nd way so that she learns that these type of problems are not always so clear and can be interpreted in more than one way.

Thats outer dimensions. But I guess I forgot to calculate bottom. There is no lid on top and aquarium is full of water.

 

[Devaraja]

Hi Devaraja. I haven't checked all your calculations, yet, but I can see your method generally, and it seems okay. However, it looks like you've forgotten about the glass bottom of the aquarium.


Based on your calculation above, you're treating 15cm as the height of the walls.

Please confirm the following.

(1) The outside dimensions are 20cm long by 25cm wide by 15cm high

(2) We're assuming that the aquarium is filled to the very brim (not realistic).

?

(1) It just say 25 x 15 x 20 I think it should be W-H-D so I guess height should be 15.
(2) Yes aquarium is filled to the very brim.

 

[Deleted member 4993]

(1) It just say 25 x 15 x 20 I think it should be W-H-D so I guess height should be 15.
(2) Yes aquarium is filled to the very brim.

So then:

Total volume of the aquarium = 25 * 20 * 15​

​

Volume of the cavity = (25-2) * (20-2) * (15-1) = volume of water \(\displaystyle \ \to \ \ \) mass of water = volume * density​

​

Volume of glass = 25 * 20 * 15 - (25-2) * (20-2) * (15-1) \(\displaystyle \ \to \ \ \) mass of glass = volume * density​

and continue....

 

[Devaraja]

T

So then:

Total volume of the aquarium = 25 * 20 * 15​

​

Volume of the cavity = (25-2) * (20-2) * (15-1) = volume of water \(\displaystyle \ \to \ \ \) mass of water = volume * density​

​

Volume of glass = 25 * 20 * 15 - (25-2) * (20-2) * (15-1) \(\displaystyle \ \to \ \ \) mass of glass = volume * density​

and continue....

Thank you very much.

 

[Otis]

… It just say 25 x 15 x 20 I think it should be W-H-D so I guess height should be 15 …

Hi Devaraja. Do you have a reason for thinking the dimensions were given as Width×Height×Depth, or did you actually guess?

If there's uncertainty, your daughter could work the exercise both ways (i.e., height=15 and height=20). That'll show the instructor she's engaged.

Also, I checked a couple videos on aquarium building, and the walls were not positioned on top of the bottom; the bottom was fit between the walls. Subhotosh's equations in post #13 are consistent with that. So, if you add the 18×23 bottom to your original work, you'll have 10.1kg total.

… 1350cm³*1000000=0.00135m³ …

… 6150cm³*1000000=0.00615m³ …

PS: Those asterisks ought to be division symbols.

 

[Devaraja]

Hi Devaraja. Do you have a reason for thinking the dimensions were given as Width×Height×Depth, or did you actually guess?

If there's uncertainty, your daughter could work the exercise both ways (i.e., height=15 and height=20). That'll show the instructor she's engaged.

Also, I checked a couple videos on aquarium building, and the walls were not positioned on top of the bottom; the bottom was fit between the walls. Subhotosh's equations in post #13 are consistent with that. So, if you add the 18×23 bottom to your original work, you'll have 10.1kg total.


PS: Those asterisks ought to be division symbols.

After some thinking I decide to go as WxDxH because WxHxD would give me almost square and shallow aquarium so WxDxH sound more realistic for aquarium,
Hopefully this is my last calculation:
Aquarium volume = 25*15*20=7500cm³
Water volume = (25-2)*(15-2)*(20-1)=5681cm³/1000000=0,005681m³
Water weight = 0,005681m³*1000kg/m³=5,681kg
Glass volume = 7500cm³-5681cm³=1819cm³/1000000=0,001819m³
Glass weight = 0,001819m³*2500kg/m³=4,547kg
Aquarium weight = 5,681kg+4,547kg=10,228kg

 

[Otis]

… 10,228kg

Hi. Very good. Now you have both versions.

It may not matter, in your daughter's class, but 10,228kg has a rounding error (10,229kg is correct). Rounding errors arise from not carrying enough digits, when rounding intermediate results.

If the students were not instructed to round the answer to the nearest 1000th of a kilogram, then 10,2kg or 10,23kg is better. (If students are expected to follow the rules of significant figures, then the correct answer is 10kg.)

The difference between 10,228kg and 10,229kg is one gram (the weight of a paperclip). So, some instructors might not care, but I'd like your daughter to be aware that future instructors will.

?