Question
Find the volume of a sphere whose surface area is $154\ cm^2.$

Answer

In the given problem,
we have to find the volume of a sphere whose surface area is given.
So, let us first find the radius of the given sphere.
Surface area of the sphere $(S) = 154\ cm^2$
Let the radius of the sphere be rcm
Now, we know that surface area of the sphere $=4\pi\text{r}^2$
So,
$154=4\Big(\frac{22}{7}\Big)(\text{r})^2$
$\text{r}^2=\frac{(154)(7)}{(4)(22)}$
$\text{r}^2=12.25$
Further, solving for $r$
$\text{r}=\sqrt{12.25}$
$\text{r}=3.5$
Therefore, the radius of the given sphere is $3.5\ cm.$
Now, the volume of the sphere $=\frac{4}{3}\pi\text{r}^3$
$=\Big(\frac{4}{3}\Big)\Big(\frac{22}{7}\Big)(3.5)^3$
$=179.66\text{ cm}^3$
Therefore, the volume of the given sphere is $179.66\ cm^3.$

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