MCQ
If the $\text{TSA}$ of a solid hemisphere is $12\pi\text{ sq.cm}$ then its $\text{CSA}$ is:
- A$2\pi\text{ sq.cm}$
- B$12\pi\text{ sq.cm}$
- ✓$8\pi\text{ sq.cm}$
- D$16\pi\text{ sq.cm}$
✓
Answer
Correct option: C.
$8\pi\text{ sq.cm}$
Given: $\text{TSA}$ of solid hemisphere $=12\pi\text{ sq.cm}$
$\Rightarrow3\pi\text{r}^2=12\pi$
$\Rightarrow\text{r}^2=4$
$\Rightarrow\text{r}=2\text{ cm}$
$\therefore \text{CSA}$ of hemisphere $=2\pi\text{r}^2=2\pi(2)^2=8\pi\text{ sq.cm}$
$\Rightarrow3\pi\text{r}^2=12\pi$
$\Rightarrow\text{r}^2=4$
$\Rightarrow\text{r}=2\text{ cm}$
$\therefore \text{CSA}$ of hemisphere $=2\pi\text{r}^2=2\pi(2)^2=8\pi\text{ sq.cm}$
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