Math, asked by tooshort6308, 1 year ago

The surface area of a sphere and a cube are equal. Prove that their volume are in the ratio 1:

Answers

Answered by 31lavneet
4

Answer:

Step-by-step explanation: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

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