MCQ
A solid is hemispherical at the bottom and conical $($of same radius$)$ above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is :
- ✓$1 : 2$
- B$2 : 1$
- C$1 : 4$
- D$4 : 1$
✓
Answer
Correct option: A.
$1 : 2$
Given that the radius of the hemisphere and the cone are equal.
Since the surface of the two parts are given to be equal.
$2\pi\text{r}^2=\pi\text{r}\text{l}$
$\Rightarrow2\text{r}=\text{l}$
$\Rightarrow\frac{\text{r}}{\text{l}}=\frac{1}{2}$
So, the ratio $1: 2$
Since the surface of the two parts are given to be equal.
$2\pi\text{r}^2=\pi\text{r}\text{l}$
$\Rightarrow2\text{r}=\text{l}$
$\Rightarrow\frac{\text{r}}{\text{l}}=\frac{1}{2}$
So, the ratio $1: 2$
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