MCQ
A hollow metallic sphere with external diameter $8\ cm$ and internal diameter $4\ cm$ is melted and moulded into a cone of base radius $8\ cm$. The height of the cone is :
- A$12\ cm$
- ✓$14\ cm$
- C$15\ cm$
- D$18\ cm$
✓
Answer
Correct option: B.
$14\ cm$
The radii of the spherical shell is $2\ cm$ and $4\ cm.$
Volume of the spherical shell $=\frac{4}{3}\pi(\text{R}^3-\text{r}^3)$
$=\frac{4}{3}\pi(4^3-2^3)$
$=\frac{4}{3}\pi(56)$
Radius of the cone $= 4\ cm$
Volume of the cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\pi(4)^2\text{h}$
$\therefore\frac{1}{3}\pi(4)^2\text{h}=\frac{4}{3}\pi(56)$
$\Rightarrow16\text{h}=4(56)$
$\Rightarrow\text{h}=14\text{ cm}$
Volume of the spherical shell $=\frac{4}{3}\pi(\text{R}^3-\text{r}^3)$
$=\frac{4}{3}\pi(4^3-2^3)$
$=\frac{4}{3}\pi(56)$
Radius of the cone $= 4\ cm$
Volume of the cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\pi(4)^2\text{h}$
$\therefore\frac{1}{3}\pi(4)^2\text{h}=\frac{4}{3}\pi(56)$
$\Rightarrow16\text{h}=4(56)$
$\Rightarrow\text{h}=14\text{ cm}$
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