Question

Three mutually tangent spheres of radius 1 rest on a horizontal plane. A sphere of radius 2 rests on them. What is the distance from the plane to the top of the larger sphere?

• A. \( 3 + \frac{\sqrt{30}}{2} \)
• B. \( 3 + \frac{\sqrt{69}}{3} \)
• C. \( 3 + \frac{\sqrt{123}}{4} \)
• D. \( \frac{52}{9} \)

Hint:

For problems involving spheres and their distances, use geometry and Pythagoras’ theorem for spatial relationships.

Answer 1

The Correct Option is B

The distance from the plane to the top of the larger sphere is calculated using the geometry of the system. The distance is found to be \( 3 + \frac{\sqrt{69}}{3} \).