Choose the correct answer from the given four options: Twelve sol… - 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 2cm and height 16cm. The diameter of each sphere is:

A
4cm
B
3cm
✓
2cm
D
6cm

✓

Answer

Correct option: C.

2cm

Given, diameter of the cylinder = 2cm$\therefore$ Radius = 1cm and height of the cylinder = 16cm
$[\because\text{diameter}=2\times\text{radius}]$
$\therefore$ 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 × 1 = 2cm
Hence, the required diameter of each sphere is 2cm.

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