2026 · Q77
A spherical metal ball is molten and made into n smaller identical spheres. In this process, the surface area of the smaller balls increases by 900%. What is the value of n?
Elementary MathematicsMensuration
- A729
- B900
- C1000
- DCannot be determined due to insufficient data
Explanation
Volume conservation gives n·r³ = R³ for the n small spheres of radius r. 'Increases by 900%' means the total surface area becomes 10 times the original: n·4πr² = 10·4πR², i.e. nr² = 10R². With r = R/n^{1/3}, n·R²/n^{2/3} = 10R² gives n^{1/3} = 10, so n = 1000, option C. Reading 'increases by 900%' as 9 times is the trap behind option A (729).