A solid is hemispherical at the bottom and conical (of same radiu… - Vidyadip

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 what will be the ratio of its radius and the slant height of the conical part?

A
$2: 1$
✓
$1: 2$
C
$3: 2$
D
$2: 3$

✓

Answer

Correct option: B.

$1: 2$

(b) : Let $r$ be the radius of hemisphere and conical part. Also, let $l$ be the slant height of conical part.
Given that, surface area of hemisphere
$=$ surface area of conical part
$\Rightarrow 2 \pi r^2=\pi r l \Rightarrow 2 r=l$
$\Rightarrow \frac{r}{l}=\frac{1}{2}$ i.e., $r: l=1: 2$

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