Question

Find the number of solid spheres, each of diameter $6cm$, that could be moulded to form a solid metallic cylinder of height $45cm$ and diameter $4cm$.

Answer 1

Solid sphere volume $v=\frac{4}{3}\pi r^3$

$rv=\frac{4}{3}\times \frac{22}{7}\times 3^{3}c{m}^3$

$rv=4\times \pi \times 9=36\pi c{m}^3$

Volume of cylinder $=\pi R^{2}h=\pi \times (\frac{4}{2}{)}^2\times 45cm$

or $v=180\pi c{m}^3$

$n=$ no of spheres $=\frac{v}{v}=\frac{180\pi c{m}^3}{36\pi c{m}^3}$

$\Rightarrow n=5$