**Results:**

- Cylinder Volume: -
- Cylinder Surface Area: -
- Cylinder Lateral Surface Area: -
- Cylinder Base Area: -

**Detailed Calculation and Explanation:**

**Formula for Volume (V):** V = π * r^{2} * h

**Formula for Surface Area (A):** A = 2 * π * r * (r + h)

**Formula for Lateral Surface Area (A _{lateral}):** A

_{lateral}= 2 * π * r * h

**Formula for Base Area (A _{base}):** A

_{base}= π * r

^{2}

**Calculations:**

- Volume (V) = -
- Surface Area (A) = -
- Lateral Surface Area (A
_{lateral}) = - - Base Area (A
_{base}) = -

A circular cylinder calculator is a tool that allows users to calculate various properties of a circular cylinder, such as its volume, surface area, and lateral surface area. Circular cylinders are common in many everyday objects, such as cans, pipes, and tanks.

**Concepts**

The following are some of the key concepts that underlie circular cylinder calculators:

**Circular cylinder:**A circular cylinder is a three-dimensional shape that consists of all points in a space that are equidistant from a given line segment, called the axis. The bases of a circular cylinder are two circles, and the axis of the cylinder is perpendicular to the bases.**Volume:**The volume of a circular cylinder is the amount of space that it occupies.**Surface area:**The surface area of a circular cylinder is the total area of its surface.**Lateral surface area:**The lateral surface area of a circular cylinder is the area of its surface, excluding the bases.

**Formulae**

The following are the formulae for calculating the volume, surface area, and lateral surface area of a circular cylinder:

**Volume:**

```
V = πr²h
```

where:

- V is the volume of the cylinder
- π is a mathematical constant with the approximate value of 3.14
- r is the radius of the cylinder base
- h is the height of the cylinder

**Surface area:**

```
S = 2πr² + 2πrh
```

where:

- S is the surface area of the cylinder
- π is a mathematical constant with the approximate value of 3.14
- r is the radius of the cylinder base
- h is the height of the cylinder

**Lateral surface area:**

```
L = 2πrh
```

where:

- L is the lateral surface area of the cylinder
- π is a mathematical constant with the approximate value of 3.14
- r is the radius of the cylinder base
- h is the height of the cylinder

**Benefits of using a circular cylinder calculator**

There are several benefits to using a circular cylinder calculator, including:

**Convenience:**Circular cylinder calculators can save users a lot of time and effort, as they can perform complex calculations quickly and accurately.**Accuracy:**Circular cylinder calculators are very accurate, as they use sophisticated mathematical algorithms to perform their calculations.**Flexibility:**Circular cylinder calculators can be used to calculate the volume, surface area, and lateral surface area of circular cylinders of any size.**Versatility:**Circular cylinder calculators can be used in a variety of fields, including engineering, mathematics, and construction.

**Interesting facts about circular cylinders**

- Circular cylinders are one of the most common shapes in engineering.
- Circular cylinders are used in a variety of everyday objects, such as cans, pipes, and tanks.
- Circular cylinders are also used in a variety of industrial applications, such as the transportation of fluids and gases.
- The largest known circular cylinder in the universe is the Great Wall of China.
- The smallest known circular cylinder in the universe is the Planck length, which is the smallest possible distance in space.

**References**

**Archimedes:**On the Sphere and Cylinder, Book II, Proposition II**Isaac Newton:**Principia Mathematica, Book III, Proposition 20**Leonhard Euler:**Introductio in Analysin Infinitorum, Volume II, Chapter 18**Carl Friedrich Gauss:**Disquisitiones Generales circa Superficies Curvas, Chapter 11**George Boole:**A Treatise on the Differential Calculus, Chapter 12

**Conclusion**

Circular cylinder calculators are a valuable tool for anyone who needs to calculate the volume, surface area, or lateral surface area of a circular cylinder. They are convenient, accurate, flexible, and versatile. Circular cylinder calculators are used in a variety of fields, including engineering, mathematics, and construction.

## Additional information

### Applications of circular cylinder calculators

Circular cylinder calculators are used in a variety of applications, including:

**Cooking:**Circular cylinder calculators can be used to calculate the volume of baking pans and other cooking utensils. This information can be used to determine the amount of ingredients needed to fill the pan and the cooking time required.**Gardening:**Circular cylinder calculators can be used to calculate the volume of flower pots and other gardening containers. This information can be used to determine the amount of soil and water needed for the plants.**Home improvement:**Circular cylinder calculators can be used to calculate the volume of paint cans and other home improvement supplies. This information can be used to determine the amount of material needed to complete a project.