Question

12 sphere of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is:

• A. $\sqrt{3}cm$
• B. $2cm$
• C. $3cm$
• D. $4cm$

Answer 1

The correct option is D $4cm$

Given that, $12$ spheres of same size are made by melting a cylinder of $16cm$ diameter and $2cm$ height.

to find out: The diameter of each sphere.

Since, the spheres are made by melting the cylinder, the volume of $12$ spheres $=$ the volume of cylinder

We know that, volume of cylinder $=\pi r^{2}h$

and volume of sphere $=\frac{4}{3}\pi r^3$

$\therefore 12\times \left(\frac{4}{3}\pi r^3\right)=\pi (8{)}^2\times 2=128\pi$

$\Rightarrow r^3=\frac{128\times 3}{12\times 4}=8$

$\Rightarrow r^3=(2{)}^3$

$\therefore r=2cm$

Hence, diameter of each sphere $=2r=4cm$.

Hence, option D is correct.