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Frustum Surface Area Calculator
Calculate truncated cone surface area, volume, and geometric properties
📚 Examples, Rules & Help
⚡Quick Examples of Frustum Surface Area
🔍How to Calculate Frustum Surface Area
🪣 Understanding Frustum Surface Area
A frustum is a truncated cone with two circular bases of different sizes connected by a curved lateral surface. It's like cutting the top off a cone parallel to the base.
Essential Formulas:
Slant Height: s = √[h² + (r₂ - r₁)²]
Top Area: A₁ = πr₁²
Bottom Area: A₂ = πr₂²
Lateral Area: A_lateral = π(r₁ + r₂)s
Total Surface Area: SA = πr₁² + πr₂² + π(r₁ + r₂)s
Volume: V = ⅓πh(r₁² + r₁r₂ + r₂²)
🌍Real-World Applications
🪣 🏗️ Engineering & Manufacturing
Structural and industrial applications
❓Frequently Asked Questions
What's the difference between a frustum and a truncated pyramid?
Frustum: Specifically refers to a truncated cone (circular bases)
Truncated Pyramid: Has polygonal bases (square, triangular, etc.)
This calculator is specifically for circular frustums (truncated cones).
How do I calculate the slant height?
The slant height forms the hypotenuse of a right triangle:
Formula: s = √[h² + (r₂ - r₁)²]
Where: h = height, r₂ = bottom radius, r₁ = top radius
It's the distance along the slanted side from one edge to the other.
🎯Common Use Cases
🏗️ Construction & Engineering
- Water tank design
- Funnel calculations
- Silo and hopper construction
- Conical roof sections
🏭 Manufacturing & Design
- Container manufacturing
- Lampshade production
- Bucket and vessel design
- Architectural elements
💡Calculator Tips & Best Practices
📏Size Constraint
Top radius must be smaller than bottom radius (r₁ < r₂) for a proper frustum.
💡Three Components
Total surface area = top circle + bottom circle + curved lateral surface.
📚 References & Further Reading
Mathematical analysis of frustum structures in construction, manufacturing, and design applications.
Engineering principles for frustum-shaped structures and their optimization in various industries
External Link
Note: These references provide additional mathematical context and verification of the formulas used in this calculator.