Cone → cylinder (same radius) — Material of a cone is reshaped into a cylinder of equal radius. If cylinder height is 5 cm, find the original cone’s height.

Introduction / Context:
Equal volume under reshaping and same radius implies a simple relation between heights using volume formulas of cone and cylinder.

Given Data / Assumptions:

• Cylinder height H_c = 5 cm
• Same radius r for both shapes
• V_cone = (1/3)πr^2h, V_cyl = πr^2H_c

Concept / Approach:
Equate volumes and solve for cone height h.

Step-by-Step Solution:
(1/3)πr^2h = πr^2H_c ⇒ h = 3H_c = 15 cm

Verification / Alternative check:
Plug back: cone volume equals cylinder volume if height triples.

Why Other Options Are Wrong:
10 or 12 cm would give smaller cone volume; 18 or 24 cm would overshoot.

Common Pitfalls:
Forgetting the 1/3 in the cone volume.

Final Answer:
15 cm