Question

If a cylinder of radius $3$cm and height of $10$cm is melted and recast into the shapes of small spheres of diameter $1$cm, then the number of spheres so formed is

• A. $135$
• B. $270$
• C. $540$
• D. $1080$

Answer 1

The correct option is C $540$

Volume of cylinder $=\pi r^{2}h$
$=\pi \times 3\times 3\times 1c{m}^3$
Volume of sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}{\left(\frac{1}{3}\right)}^3$
$=\frac{4}{3}\pi \times \frac{1}{8}=\frac{\pi }{6}c{m}^3$
$\therefore$ Number of sphere$=\frac{\pi \times 3\times 3\times 10\times 6}{\pi }=540$