A solid sphere of radius R has a total charge Q distributed evenly throughout its volume. What fraction of the total charge is located inside a radius R/2?

Volume charge density ρ = charge / volume

= Q / (4/3 πR³)

total charge is located inside a radius R/2

= volume charge density x volume of sphere of radius R/2

= [Q / (4/3 πR³) ] x 4/3 π (R/2) ³

= [Q / (4/3 πR³) ] x 4/3 πR³ x 1/8

= Q / 8

required fraction

= 1/8.