To calculate the surface area of a cone, multiply Pi (**π**) by the radius of the base (**r**). Then, multiply this result by the sum of the radius (**r**) and the square root of the sum of the square of the height (**h²**) and the square of the radius (**r²**).

## Cone Surface Area Calculator

The **Surface Area of Cone Calculator** helps you quickly determine the surface area of a cone, including both the lateral surface and the base. Using the **cone surface area formula**, the calculator can provide precise results based on the cone’s radius and slant height.

Whether you need to find the **total surface area of a cone**, the base area, or the curved surface, this tool simplifies the process. It’s perfect for students, engineers, and anyone working with geometry. The calculator can also handle specific measurements like **square feet**, **square meters**, or calculate the surface area using the **slant height**.

### Formula:

$A = \pi r \left(r + \sqrt{h^2 + r^2}\right)$

Variable | Meaning |
---|---|

A |
Surface area of the cone |

r |
Radius of the base |

h |
Height of the cone |

π |
Pi (approximately 3.14159) |

**Solved Calculations:**

**Example 1:**

**Given Values**:

**r**= 4 meters**h**= 10 meters

Calculation | Instructions |
---|---|

A = π × 4 × (4 + √(10² + 4²)) | Square the height and the radius, then find the square root of their sum. |

A = π × 4 × (4 + √(100 + 16)) | Perform the square operations and add. |

A = π × 4 × (4 + √116) | Calculate the square root. |

A = π × 4 × (4 + 10.77) | Add the results. |

A = π × 4 × 14.77 | Multiply by Pi and the radius. |

A ≈ 3.14159 × 4 × 14.77 | Multiply to get the total surface area. |

A ≈ 185.73 square meters | The result gives the total surface area. |

**Answer**: A ≈ 185.73 square meters

**Example 2:**

**Given Values**:

**r**= 6 meters**h**= 12 meters

Calculation | Instructions |
---|---|

A = π × 6 × (6 + √(12² + 6²)) | Square the height and the radius, then find the square root of their sum. |

A = π × 6 × (6 + √(144 + 36)) | Perform the square operations and add. |

A = π × 6 × (6 + √180) | Calculate the square root. |

A = π × 6 × (6 + 13.42) | Add the results. |

A = π × 6 × 19.42 | Multiply by Pi and the radius. |

A ≈ 3.14159 × 6 × 19.42 | Multiply to get the total surface area. |

A ≈ 366.52 square meters | The result gives the total surface area. |

**Answer**: A ≈ 366.52 square meters

**What is Cone Surface Area Calculator ?**

To calculate the **surface area of a cone**, you need to consider both the lateral (curved) surface and the base. The total surface area formula is **TSA = πr(l + r)**, where **r** is the radius of the base, and **l** is the slant height of the cone. Whether you’re calculating the surface area for projects in **square feet** or **square meters**, this tool makes it easy. If you know the slant height, you can easily input the values to get the total surface area without doing manual calculations.

This calculator is also versatile, allowing you to calculate the surface area for different types of cones, including **oblique cones**, **truncated cones**, and even a **cone with a hemisphere**.

For example, if you’re working with a cone and need to calculate both the base and the curved surface, the **cone surface area calculator with slant height** will provide a detailed step-by-step solution. In addition to cones, you can also explore related calculations like **pyramid surface area** or use the **cone volume calculator** for 3D geometry projects. This makes it a valuable tool for students, teachers, and professionals alike.