The volume of a cylinder is defined as the density of the cylinder which represents the amount of material it can hold or how much material can be immersed in it. The formula to calculate the volume of the cylinder is πr²h. Here, r is the radius of the cylinder and h is the height of the cylinder. The material in the cylinder could be any liquid quantity or any substance which can fill the cylinder uniformly.

 

The volume of a cylinder is measured in m³ or cubic meters.

Steps to Calculate Volume of Cylinder

The steps to calculate the volume of a cylinder is given below:

 

• Step 1:  Find out the height and the base radius of the cylinder.
• Step 2 – Substitute all the measured values in the formula of the cylinder..
• Step 3 – Calculate and write the answer in cubic meters.

Example:What would be the volume of a given cylinder having a height of 50 cm and a base radius of 21 cm?

Solution:

Given:

Height  = 50 cm

radius = 21 cm

The value of π = 22/7

we know that;

Volume of Cylinder = πr²h  cubic units

V= 227 × 21  × 21  × 50

V= 69,300

Therefore, the volume of a cylinder = 69,300 m³.

What is Cylinder in Maths?

In Mathematics, a cylinder is a three-dimensional object with two parallel bases joined by a curved surface at a fixed distance. These bases are normally circular in shape (similar to circles) and the center of two bases of the cylinder in Maths is joined by a line segment known as the axis.

Surface Area of Cylinder

The area of any shape is defined as the area covered by it in a plane. There are two types of surface in a cylinder namely a curved surface and the other is a circular basis. The area of both circular bases of cylinder is equal.

• Curved surface area (CSA) 
• Total surface area (TSA)

Curved Surface Area (CSA) of Cylinder

The curved surface area of a cylinder is defined as the area of its curved surface or the area calculated after excluding the area of its two circular bases. Curved surface area is also termed as Lateral surface area (LSA). The Curved surface area of a cylinder having its base radius ‘r’ and height ‘h’ is given by 2πrh sq. units.

Therefore, the Curved Surface Area of Cylinder Formula = 2πrh sq. units.

Total Surface Area (TSA) of Cylinder

The total surface area of a cylinder is defined as the sum of areas of the cylinder’s curved surface and two circular bases. The Total surface area of a cylinder having its base radius ‘r’ and height ‘h’ is given by:

TSA of cylinder = Curved Surface Area +  Two Circular Bases Area

                                       Or

 TSA of cylinder = Curved Surface Area of cylinder + Area of its two circular bases

                                                               = 2πrh + 2πr2 sq. units

Therefore, Total Surface Area of Cylinder = 2πr (h + r) sq. units

 

Surface Area of Cylinder Example 

Example 1:A pillar in a cylindrical shape is 50 cm in diameter and 7 m in height. Find the curved surface area of the pillar.

Solution: Given, 

Height of cylindrical pillar = 7 m

Diameter of circular base =50 cm2

Radius of Circular Base = 502= 25 cm = 0.25 m

Therefore, the CSA of  the cylindrical pillar = 2πrh sq. units

                                                                           = 2 ×227 × 0.25 × 7

                                                                           = 2 ×227×  25100 × 7

                                                                   = 11 sq. mts