How to use this calculator
- Identify the measurements labelled Total surface area S, Radius r. Check whether the figure satisfies the assumptions described below.
- Enter positive measurements in a common unit. Use the degree symbol convention for angles. Ratios such as eccentricity have no unit.
- Select Calculate. Inspect the result labels: lengths, areas and volumes have different dimensions. Copy the output or print the page if you need a record.
The formula
Total surface area S = 75.3982236862; Radius r = 3
Worked example
For Total surface area S = 75.3982236862 cm², Radius r = 3 cm, applying the displayed relationship gives radius ≈ 3 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
The radius, vertical height and slant height form a right triangle, so l² = r²+h². The total surface area includes the circular base and the curved lateral area. Volume is one-third of the matching cylinder’s volume.
Use vertical height in the volume formula. Slant height must exceed the radius for a non-degenerate right cone. Inputs are limited to 10⁹ for lengths, 10¹⁸ for areas and 10²⁷ for volumes. Extremely thin or nearly degenerate figures may lose numerical accuracy; avoid treating displayed rounding as a measurement tolerance.