Estimate the number of atoms in 1 cm3 of a solid. (note
that the diameter of an atom is about 10 ^-10 m)

Since we are not given how the atoms are packed whether it is face centered or body centered we just assume  that the atoms are just packed in a cubic manner in a sense that the atoms fills a cube. Calculations are as follows:

Volume of an atom = 4/3 πr³ = π/6 (d³) = π/6 (10^-10)³ = 5.24 x 10^-31 m³

Number of atoms = 1 cm³(1 m³ / 100³ m³) / 5.24 x 10^-31 m³ = 1.91 x 20^24 atoms