Circular Cylinder Calculator

What is a Circular Cylinder?

A circular cylinder is a three-dimensional geometric shape with two circular bases of equal size connected by a curved lateral surface. It is formed by rotating a rectangle around one of its sides. Cylinders are common in everyday life, from cans and pipes to architectural columns.

How to Calculate Cylinder Properties

To fully understand a circular cylinder, we need to calculate several key properties: its radius, height, lateral surface area, total surface area, and volume. Each of these properties provides unique information about the cylinder's dimensions and characteristics.

Formulas

Here are the essential formulas for a circular cylinder:

1. Volume (V):

\[ V = \pi r^2 h \]

2. Lateral Surface Area (L):

\[ L = 2\pi r h \]

3. Total Surface Area (A):

\[ A = 2\pi r h + 2\pi r^2 = 2\pi r(h + r) \]

Where:

• \(r\) is the radius of the circular base
• \(h\) is the height of the cylinder
• \(\pi\) is the mathematical constant pi (approximately 3.14159)

Calculation Steps

1. Determine the radius (r) and height (h) of the cylinder
2. Calculate the volume using \(V = \pi r^2 h\)
3. Calculate the lateral surface area using \(L = 2\pi r h\)
4. Calculate the total surface area using \(A = 2\pi r(h + r)\)

Example and Visual Representation

Let's calculate the properties of a cylinder with a radius of 3 units and a height of 5 units:

1. Given: \(r = 3\) units, \(h = 5\) units
2. Volume: \(V = \pi r^2 h = \pi (3^2)(5) \approx 141.37\) cubic units
3. Lateral Surface Area: \(L = 2\pi r h = 2\pi (3)(5) \approx 94.25\) square units
4. Total Surface Area: \(A = 2\pi r(h + r) = 2\pi (3)(5 + 3) \approx 150.80\) square units

Here's a visual representation of this cylinder:

In this diagram, you can see a 2D representation of our cylinder with radius 3 units and height 5 units. The blue surface represents the cylinder's lateral surface, the red dashed line shows the radius, and the green dashed line shows the height. The radius (r), height (h), volume (V), total surface area (A), and lateral surface area (L) are labeled.