Question
If the total surface area of a solid hemisphere is 462cm, find its volume.
✓
Answer
Total surface area of solid hemisphere $=3\pi\text{r}^2$
$\Rightarrow462=3\pi\text{r}^2$
$\Rightarrow462=3\times\frac{22}{7}\times\text{r}^2$
$\Rightarrow462=\frac{66}{7}\times\text{r}^2$
$\Rightarrow\text{r}^2=\frac{3234}{66}$
$\Rightarrow\text{r}^2=49$
$\Rightarrow\text{r}=7\text{cm}$
Now,
Volume of a solid hemisphere $=\frac{2}{3}\pi\text{r}^3$
$=\frac{2}{3}\times\frac{22}{7}\times7\times7\times7$
$=\frac{2156}{3}$
$=718.67\text{cm}^3$
$\Rightarrow462=3\pi\text{r}^2$
$\Rightarrow462=3\times\frac{22}{7}\times\text{r}^2$
$\Rightarrow462=\frac{66}{7}\times\text{r}^2$
$\Rightarrow\text{r}^2=\frac{3234}{66}$
$\Rightarrow\text{r}^2=49$
$\Rightarrow\text{r}=7\text{cm}$
Now,
Volume of a solid hemisphere $=\frac{2}{3}\pi\text{r}^3$
$=\frac{2}{3}\times\frac{22}{7}\times7\times7\times7$
$=\frac{2156}{3}$
$=718.67\text{cm}^3$
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