Cylinder → cone (same radius) — A cylinder of radius 2 cm and height 6 cm is melted into a cone of the same radius. Find the cone’s height.

Introduction / Context:Volume is conserved. With same radius, the height must adjust to preserve volume when the shape changes from cylinder to cone.

Given Data / Assumptions:

• Cylinder: r = 2 cm, h = 6 cm ⇒ V = πr^2h = 24π
• Cone: r = 2 cm, height H unknown

Concept / Approach:Set (1/3)πr^2H = 24π and solve for H.

Step-by-Step Solution:(1/3) * π * 4 * H = 24π ⇒ (4/3)H = 24 ⇒ H = 18 cm

Verification / Alternative check:Check: cone volume (1/3)*π*4*18 = 24π equals cylinder volume.

Why Other Options Are Wrong:Other values do not equate the volumes.

Common Pitfalls:Missing the 1/3 factor for cones.

Final Answer:18 cm