Question

The volume of a solid iron sphere is $\frac{2048}{3}\pi c{m}^3$. This sphere is melted and eight rings of iron plates of external radii $6\frac{2}{3}$ cm and thickness 3 cm are made. Find the internal radius of each ring.

Answer 1

Volume of cylindrical rings =Volume of sphere
$8\times \pi (R^2-r^2)\times h=\frac{2048}{3}\pi 8\times \pi \left(\right(\frac{20}{3}{)}^2-r^2)\times 3=\frac{2048}{3}\pi (\frac{20}{3}{)}^2-r^2=\frac{2048}{3\times 3\times 8}$
Solving we get r =4 cm