How would I go about finding the weight of something with the square cube law?

[PepperTeee]

I understand that to find the volume you need to multiply width, length, and height. Im just having trouble using that to find weight. So if im doing this correctly. A balck ant weigh around 5 milligrams. Now lets say we increase the size of the any by 1000. To find the weight all I have to do is multiply 5 milligrams with the volume that the enlarged ant has, right?

 

[HallsofIvy]

No, you multiply the weight by the new volume divided by the old volume. That is the same as dividing the weight by the old volume (to calculate the density) then multiplying that by new volume.

(When you say "increase the size by 1000" do you mean multiplying the volume by 1000 or multiplying each of height, width, and length by 1000?)

 

[HallsofIvy]

No, you multiply the 5 mg by the new volume divided by the old volume.

That is the same as first diving the 5 mg by the old volume (to get the density) and then multiplying by the new volume.

 

[PepperTeee]

No, you multiply the weight by the new volume divided by the old volume. That is the same as dividing the weight by the old volume (to calculate the density) then multiplying that by new volume.

(When you say "increase the size by 1000" do you mean multiplying the volume by 1000 or multiplying each of height, width, and length by 1000?)

So I divide both volumes, and I multiply the weight by the amount that I am given from the volume?

 

[HallsofIvy]

So I divide both volumes, and I multiply the weight by the amount that I am given from the volume?

You are not being very precise!

"So I divide both volumes"
You divide the new volume by the old volume.

"and I multiply the weight by the amount that I am given from the volume?"
If by "the amount that I am given from thee volume" you mean that ratio, the new volume divided by the old volume, then yes.

Of course, all this is assuming both volumes have the same density. If that is not true the weight of one has no relation to the weight of the other.

 

[PepperTeee]

You are not being very precise!

"So I divide both volumes"
You divide the new volume by the old volume.

"and I multiply the weight by the amount that I am given from the volume?"
If by "the amount that I am given from thee volume" you mean that ratio, the new volume divided by the old volume, then yes.

Of course, all this is assuming both volumes have the same density. If that is not true the weight of one has no relation to the weight of the other.

Apologies for the late reply.

When I say divide both volumes I mean you divide the volume of the enlarged ant with the volume of the regular size ant. When I say multiply by the volume given, I mean do I multiply the weight of the smaller ant with the number that the divided volumes produced.

Can you explain what you mean by the same density? Would the ant thats larger still have the same density no matter what?

 

[HallsofIvy]

Apologies for the late reply.

When I say divide both volumes I mean you divide the volume of the enlarged ant with the volume of the regular size ant. When I say multiply by the volume given, I mean do I multiply the weight of the smaller ant with the number that the divided volumes produced.

Can you explain what you mean by the same density? Would the ant thats larger still have the same density no matter what?

If you do not assume that then it is impossible to do this problem.