Test your mathematics skills...for smarty pants!?

Question

Assume that the entire mass of an atom is
concentrated in its nucleus, a sphere of ra-
dius 1:5 £ 10¡5 pm. If the mass of an atom
is 4:22 £ 10¡22 g, what is its density? The
volume of a sphere is V =4/3pir3.
Answer in units of g=cm3.

Answer 1

A pm, or picometer is 10^(-12) meters.
1.5 x 10^(-5)pm = 1.5 x 10^(-17) meters = 1.5 x 10^(-15) cm
density = m/V
density = (4.22 x 10^(-22))/[(4/3)π(1.5 x 10^(-15))^3]
density = 2.985 x 10^22g/cm^3