Question

surface area of sphere and cube are equal prove that ratio of their volume is 1:root pie/6

Answer 1

Surface area of sphere = 4πr²
Total surface area of cube = 6a²                     (where a is side of cube)
∴ 4πr² = 6a²
   r²=6a²/4π
   r = √3a²/√2π
   r  = a√3/√2π
   Volume of sphere = 4πr³/3
   Volume of cube    = a³
   Ratio of volumes = 4πr³/3 ÷ a³
                               =4π(a√3/√2π)³/3 ÷a³                       (by putting r=a√3/√2π)
                               =(4π/3) a³ × (3/2π) × (√3/√2π) ÷ a³
                               = 2√3/√2π
                               = √2 × √3/√π = √6/√π
                               =  1 ÷ √π/√6
                               =  1 : √(π/6)
Therefore ratio of volume of sphere to volume of cube comes out to be          1 : √(π/6) 
Hence proved                  Thank you

Answer 2

HOPE THIS HELPS YOU
DIKSHA