if the number of square centimetres in the surface area of a sphere is equal to the number of cubic cm in its volume . find the diameter of sphere

Dear Student,

We know :  Surface area of sphere  =  4 $\mathrm{\pi }$r2    and Volume of sphere  =

And we take radius =  r  cm , So

Surface area of sphere  =  4 $\mathrm{\pi }$r2  cm2    and Volume of sphere  = cm3 , So from given condition we get :
= 4 $\mathrm{\pi }$r2 ,

4 $\mathrm{\pi }$r3 =12  $\mathrm{\pi }$r2 ,

r = 3

So,

Radius of given sphere  =  3 cm

Therefore ,

Diameter of given sphere  =  2 ( 3 ) =  6 cm                                                ( Ans )