Question

Suppose each of the object's three dimensions is increased by a factor of 2 without changing the material of which the object is made. By what factor will the density change

Answer 1

The density change by a factor of 0.125 if the dimensions is increased by a factor of 2

Density is the ratio of mass to the volume. It is given by:

Density (D) = mass (m) / volume (V)

Volume (V) =  length (l) * width (w) * height (h)

V = lwh

D = m/lwh

If the dimensions increased by a factor of 2:

V = 2l * 2w * 2h = 8lwh

The new density (D')

D' = m / (8lwh)

D' = 0.125D

The density change by a factor of 0.125 if the dimensions is increased by a factor of 2

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