Carbon-12 contains 6 protons and 6 neutrons. the radius of the nucleus is approximately 2.7 fm (femtometers)? and the radius of the atom is approximately 70 pm (picometers). calculate the volume of the nucleus and the volume of the atom. (assume two significant figures.) and also what percentage of the carbon atom's volume is occupied by the nucleus? (assume two significant figures.)

The shape of the atom and the nucleus is the same as the shape of the sphere, theoretically. Thus, the equation for their volumes are:

V = 4/3*πr³, where r is the radius

To be consistent with the units, let's use the SI unit meters. 1 fm = 10⁻¹⁵ m and 1 pm = 10⁻¹² m.

Volume of nucleus = 4/3*π(2.7×10⁻¹⁵)³ = 8.2×10⁻⁴⁴ m³
Volume of atom = 4/3*π(70×10⁻¹²)³ = 1.4×10⁻³⁰ m³

The percentage of nucleus in the atom is as follows:
8.2×10⁻⁴⁴ m³/1.4×10⁻³⁰ m³  * 100 = 5.9×10⁻¹² %

The nucleus of the atom occupies very little space in the atom, but is concentrated in mass. That's why the nucleus is very dense.