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be is xand the radius of sphere is r show that the surface area is ∛(4πX^2 )

Guest Mar 24, 2017
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Volume of cube  =  x^3

Volume of sphere  =   (4/3)pi* r^3

 

And

 

3(4/3)pi * r^3  =  x^3

 

4pi * r^3   =  x^3 

 

r^3  =  x^3 / [ 4pi]     take the cube root of both sides

 

r  =  x / (4pi)^(1/3)    → r^2  =  x^2 / (4pi)^(2/3)

 

Surface area of sphere  =

 

4pi * r^2  =  4pi * (x^2) / (4pi)^(2/3)  =  (4pi)^(1/3)*x^2 =  ∛[4pi] * x^2

 

 

cool cool cool

CPhill  Mar 24, 2017

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