The formula required to compute a cylinder’s cross sectional area is presented in here. The accompanying worked out examples should help you understand its usage.
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.
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.
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