MCQ
A solid metallic spherical ball of diameter $6\ cm$ is melted and recast into a cone with diameter of the base as $12\ cm.$ The height of the cone is:
- A$2\ cm$
- ✓$3\ cm$
- C$4\ cm$
- D$6\ cm$
✓
Answer
Correct option: B.
$3\ cm$
Clearly,
The volume of recasted cone $=$ volume of sphere
$\frac{1}{3}\pi\Big(\frac{12}{2}\Big)^2\times\text{h}=\frac{4}{3}\pi\Big(\frac{6}{2}\Big)^3$
$\frac{1}{3}\times36\times\text{h}=\frac{4}{3}\times27$
$\text{h}=\frac{4\times27\times3}{36}$
$\text{h}=3\text{cm}$
The volume of recasted cone $=$ volume of sphere
$\frac{1}{3}\pi\Big(\frac{12}{2}\Big)^2\times\text{h}=\frac{4}{3}\pi\Big(\frac{6}{2}\Big)^3$
$\frac{1}{3}\times36\times\text{h}=\frac{4}{3}\times27$
$\text{h}=\frac{4\times27\times3}{36}$
$\text{h}=3\text{cm}$
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