Choose the correct answer of the following question:
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
(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1
Let the radius of the hemisphere or the radius of the cone be $r$ and the slant height of the cone be $l$.
Now,
Surface area of the hemisphere = Surface area of the cone
$\Rightarrow 2 \pi r^{2}=\pi r l$
$\Rightarrow \frac{\pi r^{2}}{\pi r l}=\frac{1}{2}$
$\Rightarrow \frac{r}{l}=\frac{1}{2}$
$\therefore r: l=1: 2$
Hence, the correct answer is option (a).
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