2023 · Q69
A solid iron ball is melted and 64 smaller solid balls of equal size are made using the entire volume of iron. What is the ratio of the surface area of the larger ball to the sum of the surface areas of all the smaller balls?
Elementary MathematicsMensuration
- A0.25
- B0.5
- C0.75
- D1
Explanation
Equal volumes give 64r³ = R³, so r = R/4. The large ball's surface area is 4πR² and the 64 small balls total 64 × 4π(R/4)² = 16πR². The ratio is 4πR²/(16πR²) = 0.25 (A).