The Radius of Cone Calculator is designed to determine the base radius of a cone when certain measurements are known. It is particularly handy for quick calculations in mathematical and engineering problems, helping professionals and students alike to save time and ensure accuracy.

## Formula of Radius of Cone Calculator

#### Formula Using Volume

To find the radius of a cone’s base using its volume, the following formula is use:

r = sqrt(3V / (pi * h)) Where:

- r is the radius of the cone’s base.
- V is the volume of the cone.
- h is the height of the cone.
- pi is a constant approximately equal to 3.14159.

#### Formula Using Surface Area

To calculate the radius using the surface area of the cone, the formula is:

r = A / (pi * l) Where:

- r is the radius of the cone’s base.
- A is the surface area of the cone.
- l is the slant height of the cone.
- pi is again approximately 3.14159.

## Conversion Table for Common Measurements

Measurement | Value (in cm) | Notes |
---|---|---|

Small cone height | 10 cm | Typical height for a small cone |

Small cone volume | 314 cm³ | Volume with radius = 5 cm |

Large cone height | 50 cm | Typical height for a large cone |

Large cone volume | 3925 cm³ | Volume with radius = 14 cm |

## Example of Radius of Cone Calculator

### Scenario:

Calculate the radius of a cone with a volume of 314 cm³ and a height of 10 cm.

### Calculation:

- Use the formula: r = sqrt(3V / (pi * h))
- Substitute the values: r = sqrt(3 * 314 / (3.14159 * 10))
- Simplify the expression: r = sqrt(942 / 31.4159) = sqrt(29.979)
- Result: r = 5.477 cm

This calculation shows the radius of the cone’s base is approximately 5.477 cm.

## Most Common FAQs

**What is the most accurate way to measure the volume of a cone?**

To accurately measure the volume of a cone, you need the radius of the base and the height of the cone. The volume is then calculated using the formula V = (1/3) * pi * r^2 * h.

**How do you find the slant height of a cone if only the radius and height are known?**

The slant height (l) of a cone can be calculate using the Pythagorean Theorem, where l = sqrt(r^2 + h^2), with r being the radius and h the height of the cone.

**Can this calculator be use for truncated cones?**

Yes, the Radius of Cone Calculator can also be adapt to calculate the dimensions of a truncated cone, though the formulas will vary slightly due to the different geometric setup.