2026 · Q58
On a circular metal plate of uniform thickness, 16 holes, each of diameter 2 cm, are made. If the plate thereby has lost one-ninth of its original weight, then what is the diameter of the plate?
Elementary MathematicsMensuration
- A12 cm
- B15 cm
- C21 cm
- D24 cm
Explanation
Each hole has radius 1 cm, so the 16 holes remove area 16π·1² = 16π. Losing one-ninth of the weight means 16π = (1/9)πR², giving R² = 144 and R = 12 cm. The plate's diameter is 24 cm, option D.