A fullerene is an allotrope of carbon whose molecule consists of carbon atoms connected by single and double bonds to form a closed structure, with fused rings of five to seven atoms. Buckminsterfullerene is a type of fullerene with a molecular formula of C₆₀. The density of C₆₀ is 1.65 g/cm³. Assuming a perfect sphere that is 100 nm in diameter formed by this molecule such that the space between molecules can be neglected, calculate the approximate number of C atoms contained in one sphere of this size.