Question
If the total surface area of a solid hemisphere is $462\ cm^2$, find its volume $\Big(\text{use}\ \pi=\frac{22}{7}\Big)$
✓
Answer
Let the radius of the hemisphere be r cm.
Total surface area of hemisphere $= 462\ cm^2$
$\Rightarrow3\pi\text{r}^2=462$
$\Rightarrow3\times\frac{22}{7}\times(\text{r})^2=462$
$\Rightarrow r^2 = 49$
$\Rightarrow r = 7\ cm$
Now, the volume of hemisphere is given by
$\frac{2}{3}\pi\text{r}^3$
$=\frac{2}{3}\times\frac{22}{7}(7)^3$
$=\frac{2156}{3}$
$=718\frac{2}{8}\text{cm}^3$
Total surface area of hemisphere $= 462\ cm^2$
$\Rightarrow3\pi\text{r}^2=462$
$\Rightarrow3\times\frac{22}{7}\times(\text{r})^2=462$
$\Rightarrow r^2 = 49$
$\Rightarrow r = 7\ cm$
Now, the volume of hemisphere is given by
$\frac{2}{3}\pi\text{r}^3$
$=\frac{2}{3}\times\frac{22}{7}(7)^3$
$=\frac{2156}{3}$
$=718\frac{2}{8}\text{cm}^3$
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