Three solid spheres if radius 3cm ,4cm,5cm are melted to cast a big solid metallic sphere, find radius of the big sphere
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radius of 3 spheres = (3,4,5)cm
They are melted to form a new sphere
so volume of 3 spheres = Volume of new sphere
![\frac{4}{3} \pi( {3}^{3} + {4}^{3} + {5}^{3} ) = \frac{4}{3} \pi \: {r}^{3} \\ (27 + 64 + 125) = {r}^{3} \\ 216 = {r}^{3} \\ \sqrt[3]{216} = r \\ \huge\bold 6cm = r](https://tex.z-dn.net/?f=+%5Cfrac%7B4%7D%7B3%7D+%5Cpi%28+%7B3%7D%5E%7B3%7D++%2B++%7B4%7D%5E%7B3%7D++%2B++%7B5%7D%5E%7B3%7D+%29+%3D++%5Cfrac%7B4%7D%7B3%7D+%5Cpi+%5C%3A++%7Br%7D%5E%7B3%7D++%5C%5C+%2827+%2B+64+%2B+125%29+%3D++%7Br%7D%5E%7B3%7D++%5C%5C+216+%3D++%7Br%7D%5E%7B3%7D+%5C%5C++%5Csqrt%5B3%5D%7B216%7D++%3D+r+%5C%5C++%5Chuge%5Cbold+6cm+%3D+r "\frac{4}{3} \pi( {3}^{3} + {4}^{3} + {5}^{3} ) = \frac{4}{3} \pi \: {r}^{3} \\ (27 + 64 + 125) = {r}^{3} \\ 216 = {r}^{3} \\ \sqrt[3]{216} = r \\ \huge\bold 6cm = r")
They are melted to form a new sphere
so volume of 3 spheres = Volume of new sphere
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