Question

surface area of sphere and cube are equal.then find the ratio of their volume

Answer 1

R = radius of sphere      and        length of edge of the cube = a

Surface area of sphere =  surface area of cube
      4 π R² =  6 a²
     =>  (R/a) = √3 / √2π

Volume of sphere / volume of cube
   = (4π R³ /3)  / (a³)
   =  4π/3 *  (R/a)³ 
   =  4π/2 *   [3√3 / (2 √2 π √π) ]
   =  3 √3 /√(2π)
   ≈ 2.072