A sphere was composed of an unknown pure substance. What is the density (in g/cm^3) of the material

Question

if the sphere has a diameter of 30.79um and a mass of 25.6ng?

The volume of a spherical object is given by V = ((4/3)(Pie)(r^3)

Two demical place answer with units in the answer.

Answer 1

Density = mass / volume

It is typical to express density as g / cm3 which is the same as g / ml, so that's what we'll do.

We know the mass = 25.6 ng

So we need to find the volume:

volume of a sphere = 4/3 π r³

r = 30.79 um

converting r to cm we have 30.79 um x 1 m / 10⁶ um x 100 cm / m = 3.079x10^-4 cm

r³ = 2.92x10^-11 cm³

Volume = 4/3 x 3.14 x 2.92x10^-11 cm³

Volume = 1.22x10^-10 cm³

Now we'll convert 25.6 ng to g

25.6 ng x 1 g / 1x10⁹ ng = 2.56x10^-8 g

Density = 2.56x10^-8 g / 1.22x10^-10 cm³

Density = 209.83 g / cm³

(be sure to check all of the math)