Three spherical metal balls of radii 6cm, 8cm, r cm are melted to form a solid sphere of radius 12cm. Then the value of r is

Volume of large sphere $=$ Volumes of Individual three solids

$V=V_1+V_2+V_3$

$\frac{4}{3}\pi {\left(12\right)}^3=\frac{4}{3}\pi {\left(6\right)}^3+\frac{4}{3}\pi {\left(8\right)}^3+\frac{4}{3}\pi r^3$

$\frac{4}{3}\pi {\left(12\right)}^3=\frac{4}{3}\pi \left(6^3+8^3+r^3\right)$

${\left(12\right)}^3=6^3+8^3+r^3$

$1728=216+512+r^3$

$1728=728+r^3$

$1728-728=r^3$

$1000=r^3$

$r=\sqrt[3]{1000}$

$\therefore r=10$ cm