A solid cylinder of radius 3 cm and height 5 cm is melted to form tiny right circular cones, each with base radius 1 mm and height 1 cm. How many such cones can be made?

Introduction / Context:
Melting and recasting conserves volume. We compute the cylinder volume and divide by the volume of one small cone to find the count of cones produced.

Given Data / Assumptions:

• Cylinder: r = 3 cm, h = 5 cm → V_cyl = πr^2h.
• Cone: base radius = 1 mm = 0.1 cm, height = 1 cm → V_cone = (1/3)πr^2h.

Concept / Approach:
Number of cones n = V_cyl / V_cone (volumes in the same units). Convert millimetres to centimetres before substitution.

Step-by-Step Solution:

Verification / Alternative check:
π cancels; ensure radius in cm (0.1 cm) to avoid 100× error.

Why Other Options Are Wrong:
They arise from unit mistakes (using 1 mm as 1 cm) or misplacing the 1/3 in cone volume.

Common Pitfalls:
Unit conversion errors; forgetting the 1/3 factor for cone volume; arithmetic slips during division.

Final Answer:
13500