Is my mass calculation method correct?

[5P@N]

Homework Statement

I have an object of a known mass, and known dimension along one axis (length).
Mass: 10 kg
Length: 2 meters

I wish to calculate what the mass of an object that is similarly constituted and shaped will be if it has a greatly expanded length of: 1,000 meters.

I am seeking to know what the mass of this larger object will be.

Homework Equations

Volume = Length * Width * Height

Conversion factor = larger object / smaller object

{ (conversion factor)^3 } * mass of smaller object = mass of larger object
(The conversion factor is cubed so as to account for all 3 volumetric dimensions of expansion)

The Attempt at a Solution

1,000 m / 2 m = 500
500 = conversion factor
(500)^3 = 125,000,000

This 125 million is then multiplied by the original mass of 10 kg, to get an answer of: 1 billion, 250 million kg.

Does anybody see a problem with my result and/or logic? Reply if you do.

 

[haruspex]

Homework Statement

I have an object of a known mass, and known dimension along one axis (length).
Mass: 10 kg
Length: 2 meters

I wish to calculate what the mass of an object that is similarly constituted and shaped will be if it has a greatly expanded length of: 1,000 meters.

I am seeking to know what the mass of this larger object will be.

Homework Equations

Volume = Length * Width * Height

Conversion factor = larger object / smaller object

{ (conversion factor)^3 } * mass of smaller object = mass of larger object
(The conversion factor is cubed so as to account for all 3 volumetric dimensions of expansion)

The Attempt at a Solution

1,000 m / 2 m = 500
500 = conversion factor
(500)^3 = 125,000,000

This 125 million is then multiplied by the original mass of 10 kg, to get an answer of: 1 billion, 250 million kg.

Does anybody see a problem with my result and/or logic? Reply if you do.

Looks fine to me.

 

[Mister T]

You want to make it 500 times longer, wider, and thicker, so it will have a volume that's ##(500)^3## times bigger. Assuming you keep the density of the object the same, the mass will increase by the same factor:$$10 \ \mathrm{kg} \times (500)^3=1.25 \times 10^9 \ \mathrm {kg}$$