# Circular Cylinder Calculator

The Circular Cylinder Calculator is a tool that allows you to calculate various properties of a cylinder given two known values. It is commonly used in engineering, construction, and other fields that require calculations involving cylinders.

## Concepts

### Cylinder

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases connected by a curved surface. The height of the cylinder is the perpendicular distance between the two bases.

## Formulae

The Circular Cylinder Calculator uses the following standard formulas for a cylinder:

### Volume

The volume of a cylinder is given by the formula:

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``````V = πr^2h
``````

where `r` is the radius of the circular base and `h` is the height of the cylinder.

### Lateral Surface Area

The lateral surface area of a cylinder is given by the formula:

``````L = 2πrh
``````

where `r` is the radius of the circular base and `h` is the height of the cylinder.

### Top and Bottom Surface Area

The top and bottom surface area of a cylinder are both equal to the area of a circle with radius `r`. Therefore, they are given by the formula:

``````T = B = πr^2
``````

### Total Surface Area

The total surface area of a cylinder is given by the formula:

``````A = L + T + B = 2πrh + 2πr^2 = 2πr(h + r)
``````

## Benefits

The Circular Cylinder Calculator has several benefits:

• Accuracy: The calculator applies correct formulas for each calculation.
• Versatility: The calculator outputs volume, lateral surface area, top surface area, bottom surface area, and total surface area from two known values.
• Consistency: The calculator standardizes calculations between problems.
• Accessibility: The calculator removes mental math barriers to multi-property calculation.
• Applications: The calculator supports dimensions across scales for design, construction, etc.

## Interesting Facts

• A cylinder is one of the most basic geometric shapes and can be found in many everyday objects such as cans, pipes, and glasses.
• The volume of a cylinder was first calculated by Archimedes in ancient Greece.
• The formula for calculating the volume of a cylinder was first written down by Euclid in his book “Elements”.
• The surface area of a cylinder can be used to calculate its heat transfer properties in thermodynamics.

## Scholarly References

Here are some scholarly references that you may find useful:

• Weisstein, Eric W. “Cylinder.” MathWorld. 2
• Bhattacharya, S., et al. “Heat Transfer from Cylinders in Crossflow.” Journal of Heat Transfer, vol. 123, no. 3, 2001, pp. 547–558. 3
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