Surface Area of A Cone Without Height Calculator

Introduction

Calculating the surface area of a cone is a common geometry problem. When you know the radius and slant height of a cone, you can find its total surface area without needing the height. This calculator provides an easy way to compute this value.

The surface area of a cone includes both the base area and the lateral (side) area. The formula accounts for the circular base and the curved surface that wraps around the base.

Formula

The total surface area (A) of a cone can be calculated using the following formula when you know the radius (r) and slant height (l):

Where:

• A is the total surface area
• r is the radius of the base
• l is the slant height
• π (pi) is approximately 3.14159

This formula combines the area of the circular base (πr²) with the lateral area (πrl).

Calculation

To calculate the surface area of a cone:

1. Measure or determine the radius of the cone's base (r).
2. Measure or determine the slant height (l) of the cone.
3. Square the radius (r²).
4. Multiply the squared radius by π to get the base area (πr²).
5. Multiply the radius by the slant height (rl).
6. Multiply this product by π to get the lateral area (πrl).
7. Add the base area and lateral area together to get the total surface area.

Use our calculator above to perform these steps quickly and accurately.

Example

Let's calculate the surface area of a cone with a radius of 5 cm and a slant height of 13 cm.

1. Base area: π × 5² = π × 25 ≈ 78.54 cm²
2. Lateral area: π × 5 × 13 ≈ 204.20 cm²
3. Total surface area: 78.54 + 204.20 ≈ 282.74 cm²

So, the surface area of this cone is approximately 282.74 square centimeters.