Question

A trash compactor can compress its contents to 0.350 times their original volume. Neglecting the mass of air expelled, by what factor is the density of the rubbish increased?

a) 1.35
b) 2.86
c) 3.57
d) 4.42

Answer 1

The density of the rubbish in a trash compactor that reduces the volume to 0.350 of the original is increased by a factor of 2.86 times.

Step-by-step explanation:

When a trash compactor reduces the volume of its contents to 0.350 of their original volume, the density of the rubbish is increased because the mass remains constant while the volume decreases. Density is defined as mass per unit volume (ρ = m/V). If the original volume is V and the new volume is 0.350V, then the new density (ρ2) will be:

ρ2 = m / (0.350V)

The original density (ρ1) is m/V. To find by what factor the density has increased, we divide the new density by the original density:

Factor = ρ2 / ρ1

Factor = (m / (0.350V)) / (m/V)

Factor = 1 / 0.350

Factor = 2.86

Therefore, the density of the rubbish is increased by a factor of 2.86 times.