**Instructions:**

- Enter the top radius (r1), bottom radius (r2), and height (h) of the conical frustum.
- Select the unit of measurement from the dropdown.
- Click "Calculate" to calculate the volume and surface area of the frustum.
- Results will be displayed below along with detailed calculations.
- Use the "Clear" button to reset the inputs and results.
- Click "Copy" to copy the results to the clipboard.

**Results:**

**Detailed Calculation:**

**Calculation History:**

The **Conical Frustum Calculator** is a tool that helps you calculate the various properties of a conical frustum given any two known variables. It is a simple and easy-to-use tool that can be used by anyone who has basic knowledge of geometry.

## Concepts

The concept of calculating the properties of a conical frustum is based on the idea of finding the volume, surface area, slant height, and other properties of a conical frustum. The calculator does this for us automatically.

## Formulae

The formulae used by the calculator to calculate the properties of a conical frustum are as follows:

### Volume

```
V = (1/3)πh(r1^2 + r2^2 + r1r2)
```

where `V`

is the volume of the conical frustum, `h`

is the height of the conical frustum, `r1`

is the radius of the top base of the conical frustum, and `r2`

is the radius of the bottom base of the conical frustum.

### Surface Area

```
A = π(r1 + r2)l + πr1^2 + πr2^2
```

where `A`

is the surface area of the conical frustum, `r1`

is the radius of the top base of the conical frustum, `r2`

is the radius of the bottom base of the conical frustum, and `l`

is the slant height of the conical frustum.

### Slant Height

```
l = √((r1 - r2)^2 + h^2)
```

where `l`

is the slant height of the conical frustum, `r1`

is the radius of the top base of the conical frustum, `r2`

is the radius of the bottom base of the conical frustum, and `h`

is the height of the conical frustum.

## Benefits

The **Conical Frustum Calculator** has several benefits, including:

### Accuracy

The calculator is very accurate and can calculate the properties of a conical frustum with a high degree of precision. It eliminates the possibility of human error in calculations.

### Speed

The calculator is fast and can calculate the properties of a conical frustum in a matter of seconds. This saves time and effort, especially when dealing with large conical frustums.

### Understanding

The calculator helps users understand the concept of calculating the properties of a conical frustum. It shows the steps involved in finding the volume, surface area, slant height, and other properties of a conical frustum.

### Real-life Applications

The concept of calculating the properties of a conical frustum is used in many real-life situations, such as architecture, engineering, and construction. The calculator helps users apply this concept in practical situations.

## Interesting Facts

Here are some interesting facts about conical frustums:

- A conical frustum is a three-dimensional geometric shape that tapers smoothly from a flat top base to a flat bottom base.
- The volume of a conical frustum is exactly one-third the volume of a right circular cone with the same height and base radii.
- The ancient Egyptians and Greeks used conical frustums in their architecture and art.
- The conical frustum is one of the oldest and most basic geometric shapes, and mathematicians have studied it for thousands of years.

**References**

Here are some scholarly references that you may find useful:

- Weisstein, E. W. (2022). Conical Frustum. Wolfram MathWorld
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Last Updated : 25 November, 2023

Emma Smith holds an MA degree in English from Irvine Valley College. She has been a Journalist since 2002, writing articles on the English language, Sports, and Law. Read more about me on her bio page.