How would the densities of a cube and a sphere be compared if.. (Below)?

Question

How would the densities of a cube and a sphere be compared if the masses of the cube and sphere had been the same, but the volume of the cube had been greater?

Answer 1

Density = Mass/ Volume.

Now you stated the Masses of the cube and sphere are the same so we make that just a number M for both.
D(sphere) = M / V(sphere)
D(cube) = M /V(cube) where V(cube) > V(sphere)
The density of M/V(cube) is a smaller number (or less density) than M/V(sphere)
QED

Answer 2

Density is a measure of mass per unit volume. It's the amount of mass there is within a specific volume of a substance. Essentially, it'd be if you divided the mass by the volume.


The masses of the cube and sphere are the same, but the volume of the cube is greater. Let's assign some random numbers to this; we'll say the cube and sphere both have a mass of 10, the cube's volume is 5, and the sphere's volume is 2.

Density of cube: 10/5 = 2.
Density of sphere: 10/2 = 5.

So, the sphere's density should be higher, since it has the same amount of mass within a smaller amount of volume.