Question

if the value of sphere is equal to its surface area find the diameter of the sphere​

Answer 1

${\huge{\underline{\underline{\rm{Question}}}}}$

If the volume of a sphere is equals to its surface area, then find its diameter.

${\huge{\underline{\underline{\rm{Solution}}}}}$

Volume of sphere=$\rm \large \frac{4}{3} \pi {r}^{3}$

Surface area=$\rm \large4\pi {r}^{2}$

${\rm {\large {\boxed{\frac{4}{3} \pi {r}^{3} = 4\pi {r}^{2}}}}} \\ \\ \rm \large \implies \frac{ \cancel4}{3} \times \cancel\frac{22}{7} \times \cancel{r \times r }\times r = \cancel{4 }\times \cancel\frac{22}{7} \times \cancel{r \times r} \\ \\ \implies \rm \frac{r}{3} = 1 \\ \\ \implies \rm r = 1 \times 3 = 3$

So radius =3

Diameter= Double of radius=3×2=6

So diameter of given sphere is 6 units

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