Quadratic Equation Solver (ax² + bx + c = 0)
About Cone Calculator
The Right Circular Cone & Truncated Frustum Calculator computes Volume ($V = \frac{1}{3}\pi r^2 h$), Slant Height ($l = \sqrt{r^2 + h^2}$), Total Surface Area ($TSA = \pi r(r + l)$), Lateral Curved Area ($LSA = \pi r l$), and Apex Angle ($2\arcsin(r/l)$).
How to Use Cone Calculator
Step 1
Enter two known properties (e.g. Radius and Height, or Radius and Slant Height).
Step 2
Review computed volume, slant height, surface areas, and unfolding angles.
Step 3
Click "Copy Cone Specs".
Practical Use Cases for Cone Calculator
Agricultural Grain Hopper & Funnel Capacity Sizing
Calculate storage bushels, cubic feet, and steel cone sheet cutting patterns for conical industrial hoppers and brewing vessels.
Ice Cream Cone & Traffic Pylon Manufacturing
Determine exact surface wrapper paper dimensions and volumetric fill limits for conical packaging.
Input & Output Examples
Calculating Cone with Radius 4m and Height 3m
Radius (r): `4.0 m`, Height (h): `3.0 m`
Volume: `50.2655 m³ (16π)` | Slant Height (l): `5.0 m` (3-4-5 rule) | Total Surface Area: `113.097 m² (36π)` | Lateral Area: `62.83 m²`
Key Features & Performance
- ✓Solves for: Radius, Height, Slant Height, Volume, Total Surface Area, Lateral Area, Apex Angle.
- ✓Frustum Mode: calculates truncated conical buckets with top radius ($r_1$), bottom radius ($r_2$), and height ($h$).
- ✓Flat Sector Unfolding Pattern: computes sector radius and arc angle for flat sheet metal cone fabrication.
- ✓100% Client-Side 3D geometry engine.
- ✓1-Click Copy cone dimensions.
Key Terminology & Definitions
Slant Height ($l$)
The straight-line distance along the outer surface of a cone from the perimeter of the base to the apex vertex ($l = \sqrt{r^2 + h^2}$).
Conical Frustum
The geometric solid portion of a cone remaining after cutting off the top apex with a plane parallel to the base.