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,

Please find below the solution to the asked query:

We know :  Surface area of sphere  =  4 $\mathrm{\pi }$r²    and Volume of sphere  = $\frac{4 \mathrm{\pi } r^3}{3}$

And we take radius =  r  cm , So

Surface area of sphere  =  4 $\mathrm{\pi }$r²  cm²    and Volume of sphere  = $\frac{4 \mathrm{\pi } r^3}{3}$ cm³ , So from given condition we get :
$\frac{4 \mathrm{\pi } r^3}{3}$ = 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 )

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