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 $1\ mm$. The value of $n$ is.
- A$450$
- B$4500$
- ✓$13500$
- D$1350$
✓
Answer
Correct option: C.
$13500$
Radius of cylinder $= 3\ cm.$
Height $= 5\ cm$
Radius of cone$= 1\ mm = 0.1\ cm$
Height $= 1\ cm$
Volume of cylinder $=$ number of cones $×$ Volume of cone
$\pi\text{R}^2\text{h}=\text{n}\times\frac{1}{3}\pi\text{r}^2\text{h}$
$\pi32\times5=\text{n}\times\frac{1}{3}\pi\times0.1^2\times1$
$45=\text{n}\times\frac{1}{3}\times(.1)^2\times1$
$45=\text{n}\times\frac{1}{100}$
$\text{n}=13500$
$13500$
Height $= 5\ cm$
Radius of cone$= 1\ mm = 0.1\ cm$
Height $= 1\ cm$
Volume of cylinder $=$ number of cones $×$ Volume of cone
$\pi\text{R}^2\text{h}=\text{n}\times\frac{1}{3}\pi\text{r}^2\text{h}$
$\pi32\times5=\text{n}\times\frac{1}{3}\pi\times0.1^2\times1$
$45=\text{n}\times\frac{1}{3}\times(.1)^2\times1$
$45=\text{n}\times\frac{1}{100}$
$\text{n}=13500$
$13500$
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