Twelve solid spheres of the same size are made by melting a solid…

MCQ

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2\ cm$ and height $16\ cm.$ The diameter of each sphere is :

✓
$2\ cm$
B
$3\ cm$
C
$4\ cm$
D
$6\ cm$

✓

Answer

Correct option: A.

$2\ cm$

Radius of the cylinder $=\frac{2}{2}=1\text{ cm}$
$\text{h}=16\text{ cm}$
Since twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2\ cm$ and height $16\ cm,$
$12\times\frac{4}{3}\pi\text{r}^3=\pi\text{R}^2\text{h}$
$\Rightarrow12\times\frac{4}{3}\text{r}^3=\text{R}^2\text{h}$
$\Rightarrow12\times\frac{4}{3}\times\Big(\frac{\text{d}}{2}\Big)^3=(1)^2\times16$
$\Rightarrow16\times\Big(\frac{\text{d}}{2}\Big)^3=(1)^2\times16$
$\Rightarrow\Big(\frac{\text{d}}{2}\Big)^3=1$
$\Rightarrow\frac{\text{d}^3}{8}=1$
$\Rightarrow\text{d}^3=8$
$\Rightarrow\text{d}=\pm2$
Since the diameter connot be negative $, d = 2\ cm.$

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