Question
The volume of a hemisphere is $2425\frac{1}{2}\text{cm}^3.$ find its curved surface area.
✓
Answer
Let r be the radius the hemisphere.
now, volume of hemisphere $2425\frac{1}{2}\text{cm}^3$
$\Rightarrow\frac{2}{3}\pi\text{r}^3=\frac{4851}{2}$
$\Rightarrow\frac{2}{3}\times\frac{22}{7}\times\text{r}^3=\frac{4851}{2}$
$\Rightarrow\frac{44}{21}\times\text{r}^3=\frac{4851}{2}$
$\Rightarrow\text{r}^3=\frac{4851\times21}{88}$
$\Rightarrow\text{r}=\sqrt[3]{1157.625}$
$\Rightarrow\text{r}=10.5\text{cm}$
Now,
Cueved surface area $2\pi\text{r}^2$
$=2\times\frac{22}{7}\times(10.5)^2$
$=\frac{44}{7}\times110.25$
$=693\text{cm}^2$
now, volume of hemisphere $2425\frac{1}{2}\text{cm}^3$
$\Rightarrow\frac{2}{3}\pi\text{r}^3=\frac{4851}{2}$
$\Rightarrow\frac{2}{3}\times\frac{22}{7}\times\text{r}^3=\frac{4851}{2}$
$\Rightarrow\frac{44}{21}\times\text{r}^3=\frac{4851}{2}$
$\Rightarrow\text{r}^3=\frac{4851\times21}{88}$
$\Rightarrow\text{r}=\sqrt[3]{1157.625}$
$\Rightarrow\text{r}=10.5\text{cm}$
Now,
Cueved surface area $2\pi\text{r}^2$
$=2\times\frac{22}{7}\times(10.5)^2$
$=\frac{44}{7}\times110.25$
$=693\text{cm}^2$
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