MCQ
A solid metallic cylinder of base radius $3\ cm$ and height $5\ cm$ is melted to make $n$ solid cones of height $1\ cm$ and base radius $1mm.$ The value of $n$ is:
- A$450$
- B$1350$
- C$4500$
- ✓$13500$
✓
Answer
Correct option: D.
$13500$
$n =$ number of cones $=\frac{\text{Volume}\ \text{of}\ \text{the}\ \text{cylinder}}{\text{Volume}\ \text{of}\ \text{one}\ \text{cone}}$
$=\frac{\pi(3)^2\times5}{\frac{1}{3}\pi\Big(\frac{1}{10}\Big)^2\times1}$
$=\frac{9\times5}{\frac{1}{3}\times\frac{1}{100}}$
$=\frac{45}{\frac{1}{300}}$
$=45\times300$
$=13500$
$=\frac{\pi(3)^2\times5}{\frac{1}{3}\pi\Big(\frac{1}{10}\Big)^2\times1}$
$=\frac{9\times5}{\frac{1}{3}\times\frac{1}{100}}$
$=\frac{45}{\frac{1}{300}}$
$=45\times300$
$=13500$
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