Question

# If a solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each, then n = _________.

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Solution

## Radius of the solid sphere, R = 4 cm Radius of each solid hemisphere, r = 2 cm It is given that, the solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each. ∴ n × Volume of each solid hemisphere = Volume of the sphere $⇒n×\frac{2}{3}\mathrm{\pi }{r}^{3}=\frac{4}{3}\mathrm{\pi }{R}^{3}$ $⇒n=2×\frac{{R}^{3}}{{r}^{3}}$ $⇒n=2×{\left(\frac{R}{r}\right)}^{3}$ $⇒n=2×{\left(\frac{4\mathrm{cm}}{2\mathrm{cm}}\right)}^{3}$ (R = 4 cm and r = 2 cm) $⇒n=2×8$ $⇒n=16$ Thus, the value of n is 16. If a solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each, then n = ___16___.

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