A solid sphere of radius 28 m is melted and recast into 8 equal solid spheres. What is the sum of the surface areas of the 8 small spheres? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 19712 m2
Melting and recasting keeps the volume the same. The volume of a sphere is \(\displaystyle \frac{4}{3}\pi r^3\) and its surface area is \(4\pi r^2\).
\(\displaystyle 8\times\frac{4}{3}\pi r^3=\frac{4}{3}\pi\times28^3\), so \(\displaystyle r^3=\frac{28^3}{8}\)
\(\displaystyle r=\frac{28}{2}=14\) m
Surface area of one small sphere \(\displaystyle =4\times\frac{22}{7}\times14\times14=2464\) m2
Sum for 8 spheres \(=8\times2464=19712\) m2