A hemispherical basin of diameter 150 cm holds 120 times the volume of a cylindrical tube. If the height of the tube is 15 cm, find the diameter (in cm) of the tube.

Introduction / Context:Relate the hemisphere’s volume to a multiple (120×) of a cylinder’s volume to solve for the cylinder’s radius, then double it to get the diameter.

Given Data / Assumptions:

• Hemisphere radius R = 150/2 = 75 cm.
• Hemisphere volume V_h = (2/3)πR^3.
• Cylinder height h = 15 cm; cylinder radius = r (unknown).
• V_h = 120 × V_cylinder = 120 × πr^2h.

Concept / Approach:Set (2/3)πR^3 = 120πr^2h, cancel π, solve for r, then diameter = 2r.

Step-by-Step Solution:

Verification / Alternative check:Square root of 156.25 is exactly 12.5; substitution confirms equality.

Why Other Options Are Wrong:24, 26, 27 cm are near but not exact; they fail the volume equality.

Common Pitfalls:Using sphere instead of hemisphere volume; forgetting to double the radius to get diameter; arithmetic slips with large cubes.

Final Answer:25 cm