Conical Frustum Calculator
Find the properties of a truncated cone. This tool provides the volume and surface area for any conical frustum given the top and bottom radii.
Volume (V) = (1/3) × π × h × (R² + Rr + r²)
R=10, r=5, h=12: V = (1/3) * π * 12 * (100 + 50 + 25) = 4 * π * 175 ≈ 2199.11
What is a conical frustum?
A conical frustum is the portion of a cone that remains after its top has been cut off by a plane parallel to its base.
How do I calculate the volume of a frustum?
The volume formula is V = (1/3) × π × h × (R² + Rr + r²), where R is the radius of the large base, r is the radius of the small base, and h is the vertical height.
What is the surface area of a conical frustum?
The total surface area includes the top and bottom circles plus the lateral area. Formula: SA = π(R² + r² + (R+r) × s), where s is the slant height.
How do I find the slant height?
Slant height (s) is calculated using the vertical height (h) and the difference in radii: s = √(h² + (R - r)²).
🔗 Related Calculators
📐 Formula
Volume (V) = (1/3) × π × h × (R² + Rr + r²)
📝 Example Calculation
R=10, r=5, h=12: V = (1/3) * π * 12 * (100 + 50 + 25) = 4 * π * 175 ≈ 2199.11
❓ Frequently Asked Questions
What is a conical frustum?▼
A conical frustum is the portion of a cone that remains after its top has been cut off by a plane parallel to its base.
How do I calculate the volume of a frustum?▼
The volume formula is V = (1/3) × π × h × (R² + Rr + r²), where R is the radius of the large base, r is the radius of the small base, and h is the vertical height.
What is the surface area of a conical frustum?▼
The total surface area includes the top and bottom circles plus the lateral area. Formula: SA = π(R² + r² + (R+r) × s), where s is the slant height.
How do I find the slant height?▼
Slant height (s) is calculated using the vertical height (h) and the difference in radii: s = √(h² + (R - r)²).