2020 · Q87
Out of 4 identical balls of radius r, 3 balls are placed on a plane such that each ball touches the other two balls. The 4th ball is placed on them such that this ball touches all the three balls. What is the distance of centre of 4th ball from the plane?
Elementary MathematicsMensuration
- A2√(2/3) r unit
- B(√3 + 2√2)/√2 r unit
- Cr/(3 − 2√2) unit
- D(√3 + 2√2)/√3 r unit
Explanation
The three base centres form an equilateral triangle of side 2r, whose centroid is 2r/√3 from each. The 4th centre is √(4r² − 4r²/3) = 2r√(2/3) above their plane, i.e. r + 2r√(2/3) = (√3 + 2√2)/√3 · r above the table.