Question

If a solid hemisphere of radius 8 cm is melted and recast into n spheres of radius 2 cm each, then n = _________.

Answer 1

Radius of the solid hemisphere, R = 8 cm

Radius of each sphere, r = 2 cm

It is given that, solid hemisphere of radius 8 cm is melted and recast into n spheres of radius 2 cm each.

∴ n × Volume of each sphere = Volume of the solid hemisphere

$\Rightarrow n\times \frac{4}{3}\mathrm{\pi }{r}^3=\frac{2}{3}\mathrm{\pi }{R}^3$

$\Rightarrow n=\frac{1}{2}\left(\frac{R^3}{r^3}\right)$

$\Rightarrow n=\frac{1}{2}{\left(\frac{R}{r}\right)}^3$

$\Rightarrow n=\frac{1}{2}\times {\left(\frac{8\mathrm{cm}}{2\mathrm{cm}}\right)}^3$ (R = 8 cm and r = 2 cm)

$\Rightarrow n=\frac{1}{2}\times 64$

$\Rightarrow n=32$

Thus, the value of n is 32.

If a solid hemisphere of radius 8 cm is melted and recast into n spheres of radius 2 cm each, then n = ___32___.