Question

Say that you have ten ball bearings, each having a mass of 1.234 g and a density of 3.1569 g/cm3. Calculate the volume of these ten ball bearings in liters (L)

Answer 1

In 3 dimensions, the volume inside a sphere (that is, the volume of a ball) is derived to be

$$V = \frac {4}{3} \pi r ^ {3}$$

where $r$ is the radius of the sphere and $\pi$ is the constant pi. But in your case it is even easier, because it is possible to find volume from mass and density:

Density is of a material is its mass per unit volume. The symbol most often used for density is $\rho$ (the lower case Greek letter rho). Mathematically, density is defined as mass divided by volume:

$$\rho = \frac {m}{V},$$

From this equation $\mathrm{V} = \mathrm{m} / \rho$

$$\mathrm {V} = 1.234 \mathrm {g} / 3.1569 \mathrm {g} / \mathrm {cm} ^ {3} = 0,391 \mathrm {cm} ^ {3} \text { or } \mathbf {0}, \mathbf {000391 L}$$