# Cylinder Calculator

Calculate the various properties of a cylinder for given values.

Calculate the various properties of a cylinder like like volume, curved surface area(CSA) and total surface area(TSA) for given values.

## Formula:

**Volume :** [ πr²h ]

**CSA : ** [ 2πrh ]

**TSA : ** [ 2πr(h+r) ]

Where

r = radius

h = height

V = volume

π = pi = 3.1415926535898

CSA = curved surface area

TSA = total surface area

## Derivations:

**1. Curved Surface Area of Cylinder**

In order to find the area of the curved surface area of cylinder we need to know the values of radius and height having same units like mm, cm ,m , ft etc. Cylinder is a 3D structure having circular bases which are parallel to each other. The cylinder can be seen as a set of circular objects that are stacked on one another constitutes the height (h). The circular base is having radius (r) or diameter (d=2r).

Area of the curved surface = Circumference x hight

Therefore CSA = 2πr x h = 2πrh

**2. Total Surface Area of Cylinder**

As we see in picture cylinder is having one curved surface area and two circular bases (top side and bottom side or call face area).

therefore Total Surface area = Curved Surface area + Area of Circular bases.

Since there are two circular bases, therefore the area of both the circular bases = πr

^{2}+πr

^{2}= 2πr

^{2}

Now TSA = 2πrh + 2πr

^{2}

= 2πr(h + r)