Question

Twenty seven solid iron spheres each of radius 2cm are melted to form a new solid sphere. What will be the surface area of the new sphere?

Answer 1

Volume of 27 such $=\frac{27\times 32}{3}\pi cucm$
Let Radius of now sphere = R
$\therefore$ Volume of has sphere $=\frac{4}{3}\pi R^3$
$\Rightarrow \frac{4}{3}\pi R^3=\frac{27\times 32}{3}\pi$
$R^3=\frac{27\times 32}{4}=27\times 8$
$\Rightarrow R=\sqrt[3]{327\times 8}=3\times 2=6cm.$
$\therefore$ Surface Area of new sphere
$=4\pi R^2$
$=4\times \pi \times 6^2=452.39sq.cm$