Vertical Cylinder Calculator

What is a Vertical Cylinder?

A vertical cylinder is a three-dimensional geometric shape with circular bases at both ends and a straight side. It's commonly used in various industries for storage tanks, silos, and containers due to its efficient use of space and structural stability. Vertical cylinders are particularly useful for storing liquids and gases under pressure.

How to Calculate Vertical Cylinder Properties

To fully understand a vertical cylinder, we need to calculate several key properties: its radius (or diameter), height, volume, and surface area. Each of these properties provides unique information about the cylinder's dimensions and capacity.

Formulas

Here are the essential formulas for a vertical cylinder:

1. Volume (V):

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

2. Surface Area (SA):

\[ SA = 2\pi r^2 + 2\pi r h \]

Where:

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

Calculation Steps

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

Example and Visual Representation

Let's calculate the properties of a vertical cylinder with a radius of 2 meters and height of 5 meters:

1. Given: \(r = 2\) m, \(h = 5\) m
2. Volume: \(V = \pi r^2 h = \pi \times 2^2 \times 5 \approx 62.83\) cubic meters
3. Surface Area: \(SA = 2\pi r^2 + 2\pi r h = 2\pi \times 2^2 + 2\pi \times 2 \times 5 \approx 87.96\) square meters

Here's a visual representation of this vertical cylinder:

In this diagram, you can see a 2D representation of our vertical cylinder with radius 2 meters and height 5 meters. The red line shows the height, and the blue line shows the radius. The total volume (V) and surface area (SA) are labeled.