Question
Find the volume of a sphere whose surface area is $154\ cm^2. ($ Take $\pi=\frac{22}{7}).$
✓
Answer
Let the radius of the sphere be $r \ cm.$
Surface area of the sphere $= 154\ cm^2$
$\therefore4\pi\text{r}^2=154$
$\Rightarrow4\times\frac{22}{7}\times\text{r}^2=154$
$\Rightarrow\text{r}=\sqrt{\frac{154\times7}{4\times22}}=\sqrt{1225}$
$\Rightarrow\text{r}=3.5\ cm$
$\therefore$ Volume of the sphere
$=\frac{4}{3}\pi\text{r}^3=\frac{4}{3}\times\frac{22}{7}\times(3.5)^3\approx179.67\ m^3$
Thus , the volume of the sphere is approximately $179.67m^3.$
Surface area of the sphere $= 154\ cm^2$
$\therefore4\pi\text{r}^2=154$
$\Rightarrow4\times\frac{22}{7}\times\text{r}^2=154$
$\Rightarrow\text{r}=\sqrt{\frac{154\times7}{4\times22}}=\sqrt{1225}$
$\Rightarrow\text{r}=3.5\ cm$
$\therefore$ Volume of the sphere
$=\frac{4}{3}\pi\text{r}^3=\frac{4}{3}\times\frac{22}{7}\times(3.5)^3\approx179.67\ m^3$
Thus , the volume of the sphere is approximately $179.67m^3.$
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