Question

Eight spheres of same volumes are recasted by melting a metallic sphere with radius of $10cm$. Find the volume of the recasted sphere.

Answer 1

Given,Radius of the metallic sphere $\left(r\right)=10cm$
$\therefore$ Volume of sphere $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \pi \times r\times (10{)}^3$
Let the radius of each recasted spheres be R.
$\therefore$ The volume of large sphere $=8\times$ volume of spheres with radius $R$
$\begin{array}{cc}\frac{4}{3}\times \pi \times (10{)}^3& =8\times \frac{4}{3}\pi (R{)}^3\\ (10{)}^3& =(R{)}^3\times 8\\ (2R{)}^3& =(10{)}^3\\ 2R& =10\end{array}$
$R=\frac{10}{2}=5cm$
Hence, radius of the sphere casted = $5cm$.
Surface area of sphere $=4\pi R^2$
$=4\times \pi \times (5{)}^2$
$=4\times \pi \times 25$
$=100\pi {cm}^2$
Hence, surface area of casted sphere $=100\pi {cm}^2$