How it works

This calculator helps you find the total surface area of a cone, which includes the area of its circular base and its curved lateral surface. Just enter the radius and the slant height, and we'll do the math for you.

The Formula

Total Surface Area = πr(r + s) Where:
π (Pi) ≈ 3.14159
r = radius of the base
s = slant height of the cone

Worked Example

1. Example: Calculating Surface Area

   Imagine a cone with a base radius (r) of 3 cm and a slant height (s) of 5 cm. Using the formula, Total Surface Area = π * 3 * (3 + 5) = π * 3 * 8 = 24π ≈ 75.398 cm². This tool will show you this result clearly.

Tips, Assumptions & Limitations

• Ensure your radius and slant height are in the same units (e.g., both in cm or both in inches) for a consistent result.
• If you only have the height (h) and radius (r), you can find the slant height (s) using the Pythagorean theorem: s = √(r² + h²).