Choose the correct answer from the given four options : Twelve so… - Vidyadip

MCQ

Choose the correct answer from the given four options : 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 :

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

✓

Answer

Correct option: C.

$2\ cm$

Given, diameter of the cylinder $= 2\ cm$
$\therefore$ Radius $= 1\ cm$ and height of the cylinder $= 16\ cm$
$[\because\text{diameter}=2\times\text{radius}]$
$\therefore$ Volume of the cylinder $=\pi\times(1)^2\times16=16\pi\text{ cm}^3$
$\big[\because\text{volume of cylinder}=\pi\times(\text{radius})^2\times\text{height}\big]$
Now, let the radius of soild sphere $= r \ cm$
Volume of the twele solid sphere $=$ Volume of cylinder
$\Rightarrow\ \ 12\times\frac{4}{3}\pi\text{r}^3=16\pi$
$\Rightarrow\ \ \text{r}^3=1$
$\Rightarrow\ \text{r}=1\text{ cm}$
$\therefore$ Diameter of each sphere $, d = 2r = 2 \times 1 = 2\ cm$
Hence, the required diameter of each sphere is $2\ cm.$

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