A cone has a base radius of 3 cm and a height of 4 cm. If the cone is melted and recast into a sphere, what is the radius of the sphere?

Tue, 21 Apr 2026 14:02:46 +0000

**Why Curiosity About Shapes Matters in STEM and Design**
A cone has a base radius of 3 cm and a height of 4 cm. If the cone is melted and recast into a sphere, what is the radius of the sphere? This seemingly technical question reflects growing interest in geometry, material science, and real-world design — especially among students, DIY enthusiasts, and professionals exploring product development. As digital tools make visualizing shapes and transformations easier, curiosity about how solid figures relate through melting and reshaping deepens. Understanding these conversions helps demystify both mathematical principles and practical applications in manufacturing, architecture, and beyond. **A Cone Has a Base Radius of 3 cm and a Height of 4 cm. If the Cone Is Melted and Recast into a Sphere, What Is the Radius of the Sphere?
This precise inquiry combines geometry with material science, posing a challenge many find intriguing. While the melting process simplifies form, volume remains constant — the core of the calculation. Many curious users explore this not just for mechanics, but to grasp how weight and form translate across states of matter. It’s a practical problem with roots in physics and industrial design, attracting those interested in sustainability, manufacturing, and spatial reasoning.** To solve it, begin by computing the volume of the original cone. The formula for the volume of a cone is:
**V = (1/3) × π × r² × h**
Substituting r = 3 cm and h = 4 cm:
V = (1/3) × π × (3)² × (4) = (1/3) × π × 9 × 4 = 12π cm³ Since the cone is fully melted and recast into a sphere, that volume remains unchanged. The volume of a sphere is:
**V = (4/3) × π × R³**
Equating the two volumes:
12π = (4/3)πR³