Cross Sectional Area of a Cylinder

One of my personal favorite subjects of study in Geometry was calculation of area and volume of various three dimensional objects. It is an important subject in mathematics, which finds applications in engineering. Every geometrical object is distinguished by its distinct shape. This is characterized by the different surface area, volume and cross sectional area of those objects.

What is the Cross Sectional Area of a Cylinder?

When analyzing various geometrical shapes, one of the most important features considered is the cross sectional area. A cross section is a perpendicular section of any geometrical object, which is taken perpendicular to the longest axis passing through it. A cylinder could be defined as a three dimensional surface created by equidistant points from a line segment extending in space. A plumbing pipe piece is an example of a cylindrical object.

The cross section of a cylinder will be perpendicular to the longest axis passing through the center of the cylinder. Imagine a circular object like a pipe and cutting it in a perpendicular slice to its length. What will be the shape of the cross section. Considering that the cylinder has two circular faces on both ends, the shape of the cross section is bound to be a circle. A thin cross sectional slice of a cylinder is going to be a circle and therefore the cross sectional area formula of a cylinder is going to be same as the formula for area of a circle.

Formula

As explained in the previous paragraph, when you cut a thin perpendicular slice of a cylinder, to the long axis, what you essentially get is a circle. Hence, the formula for cross sectional area is going to be the same as the formula for area of a circle. So here's the formula:

Cross Sectional Area of a Cylinder = π x R²

where π is a constant (= 3.14159265) which is the ratio of the circumference to diameter of a circle, while R is the radius of the cylinder. So all you need to know, to be able to calculate the cross sectional area is its radius. The square of the radius, multiplied by π, shall give you the value of the cross sectional area. The unit of cross sectional area will depend on the length unit used for radius measurement. Since π is dimensionless, the unit for area could be meter², cm² or even ft².

Solved Example

Problem: Consider a cylinder with a radius of 3 meters and a height of 6 meters. What will be the cross sectional area of this cylinder?

Solution: Using the above formula for calculation, the value of cross sectional area will be:

Cross Sectional Area = π x (3 meter)² = 3.14159265 x 9 = 28.2743385 m²

Remember the area of a circle formula - 'πr²', which will give you the cross sectional area of a right circular cylinder of any dimension.