# 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

Please find below the solution to the asked query:

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

*r*

^{2}and Volume of sphere = $\frac{4\mathrm{\pi}{r}^{3}}{3}$

And we take radius =

*r*cm , So

Surface area of sphere = 4 $\mathrm{\pi}$

*r*

^{2}cm

^{2}and Volume of sphere = $\frac{4\mathrm{\pi}{r}^{3}}{3}$ cm

^{3}, So from given condition we get :

$\frac{4\mathrm{\pi}{r}^{3}}{3}$ = 4 $\mathrm{\pi}$

*r*

^{2},

4 $\mathrm{\pi}$

*r*

^{3}=12 $\mathrm{\pi}$

*r*

^{2},

*r*= 3

So,

Radius of given sphere = 3 cm

Therefore ,

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

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