A conical frustum is what you get when you slice a cone parallel to its base.
About this calculator
A conical frustum is what you get when you slice a cone parallel to its base. Enter the top radius, bottom radius, and vertical height to get volume and surface area.
Example: bottom R = 4, top r = 2, height h = 6 gives V = (π×6/3)(16 + 8 + 4) = 56π ≈ 175.93 cubic units.
Use this for tapered tanks, lamp shades, and silo sections. Link to [[cone]] for a full cone, [[cylinder]] when top and bottom radii match, and [[tank-volume]] for storage estimates.
Common uses
- Tapered storage tank or hopper volume
- Lamp shade or funnel material estimates
- Truncated cone homework in solid geometry
- Concrete pour volume for tapered forms
Frequently asked questions
What is the volume of a frustum with R=4, r=2, h=6?
V = (πh/3)(R² + Rr + r²) = (6π/3)(16 + 8 + 4) = 56π ≈ 175.93 cubic units.
What happens when top radius equals bottom radius?
The shape becomes a cylinder. Set r = R and the formula reduces to V = πR²h.
How do you find slant height?
l = √((R − r)² + h²). The lateral surface uses π(R + r)l.
Can top radius be larger than bottom radius?
Enter the larger value as bottom radius and the smaller as top radius. The calculator expects R ≥ r.