🔢 Math Calculator

📐 How It Works

Computes the volume of 3D shapes: sphere (4/3πr³), cube (a³), cylinder (πr²h), cone (1/3πr²h), and more.

🔢 Worked Examples

• Sphere r=3: V ≈ 113.1
• Cylinder r=4, h=10: V ≈ 502.7
• Cube s=5: V = 125
• Cone r=3, h=8: V ≈ 75.4

📋 Common Use Cases

• Liquid container capacity
• Concrete volume for construction
• Shipping box sizing and packing
• Medical imaging — organ volume estimation

💡 Did You Know?

Archimedes proved that the volume of a sphere is exactly 2/3 of the volume of the circumscribed cylinder (the smallest cylinder that fits around it) — a result he was so proud of that he asked it to be engraved on his tombstone.

⚠️ Common Mistake

Using the wrong formula for cone vs pyramid — a cone is 1/3 × base area × height, same as a pyramid. The base area differs: circle (πr²) for cone, polygon for pyramid.