2024 · Q43
A spherical wooden ball of radius r is to be divided into eight identical parts by cutting by planes passing through the same diameter. What is the surface area of each final piece?
Elementary MathematicsMensuration
- Aπ r²3
- B3π r²2
- C2π r²3
- D4π r²3
Explanation
Four planes through the same diameter line at 45° to each other give 8 wedge pieces. Each piece has curved area (1/8)(4πr²) = πr²/2 plus two half-disc faces 2×(πr²/2) = πr². Total = 3πr²/2 — option B (stored '3π r²2').