# All You Need to Know About Properties of Cylinder in Maths

We all know that there are two types of shapes: two-dimensional shapes and three-dimensional shapes. Two- dimensional shapes are generally ones that can be drawn on a piece of paper such as lines and curves. Three-dimensional shapes are those that can be measured in three directions: length, width, and height. Three-dimensional shapes include cubes, cuboids, cylinders, and cones.In this section, we will learn about the properties of a three-dimensional shape known as the circle.

## What is Cylinder?

Cylinders are three-dimensional geometric shapes with two parallel bases joined by a curved surface. The bases have a circular shape. This shape is found in everyday items such as pens, pencils, and cans. Here are some of the key elements of the cylinder:

• Base: A cylinder has two identical bases, one at the top and other at the bottom. The bases are circular in shape.
• Height: The height of a cylinder is equal to the perpendicular distance between two bases. It determines the cylinder’s vertical extent.
• Axis: The axis is the imaginary line passing through the center of both parallel bases. It also often referred as the height of the cylinder.
• Radius: The radius is the distance between the center of either base to its edge. It can alss be calculated as the half of the diameter. THis term is denoted as the ‘r’ or ‘d/2’.
• Curved Surface: The curved surface of the cylinder connects the two bases and wraps around the cylinder.

## What are the Properties of Cylinder?

The properties of the cylinder are as follows:

• A cylinder has two parallel bases that are always congruent and parallel to each other.
• A cylinder is a prism as it has the same cross-section everywhere.
• There is no vertex of cylinder. It means there is no specific corner present in the cylinder.
• The height of the cylinder and radius of its circular bases determines its dimensions.
• A cylinder can have two types of bases: Elliptical and Circular.

## Formulas of Cylinder

There are various formulas used to calculate the dimensions of a cylinder. We shall look at them for better understanding.

• Lateral Surface area of the cylinder: Lateral surface area excludes the area of both bases from the total surface area. It is also known as the Curved surface area of the cylinder. The formula for calculating this is as follows: 2πrh
• Total surface area of the cylinder: Total surface area of the cylinder includes the areas of both bases and the curved surface area. The formula for calculating this is as follows:

Curved surface area of the cylinder (CSA) = 2πrh

Area of Circle= πr2

Total Surface Area of cylinder= CSA+ 2x (Area of circle)

= 2πrh+2 (πr2 )

= 2πrh+ 2 πr2

= 2πr(h+r)

• Volume of the cylinder: The volume of the cylinder is the density or space that it occupies. The formula for calculating is as follows:

VOlume of cylinder= Area of circle x height

= πr2x h

=πr2h

r = radius of the cylinder

h = height of the cylinder.

π = 22/7 or 3.14

## Types of Cylinder

In geometry, cylinder can be of four types. These are described below.

• Right Cylinder: If an axis is perpendicular to the base of the cylinder, then it is called a ‘Right Cylinder’. If its both bases are circular in shape, then it is known as ‘Right Circular Cylinder’.
• Oblique Cylinder:  If one of the cylinder’s bases is displayed sideways and the axis is not at the right angle, it is referred to as an ‘Oblique Cylinder’.
• Elliptical Cylinder: If the base of a cylinder is elliptical in shape, then it is called a ‘Elliptical Cylinder’.
• Right Circular Hollow Cylinder: If a cylinder is referred to as a “right circular hollow cylinder” if it is made up of two right circular cylinders that are enclosed inside one another.

## Properties of Cylinder:Solved Examples

1. The radius of a cylinder is 3 cm and the height is 10 cm. What is the total surface area of the cylinder? Use π= 3.14

Total Surface Area of cylinder=  2πr(h+r)

= 2 x 3.14 (10+3)

=2 x3.14 x 13

=81.64 sq cm.

1. Find the lateral surface area of the cylinder, if the radius is 5cm and the height of the cylinder is 15 cm. Use π= 3.14

Lateral Surface Area of Cylinder= 2πrh

= 2 x 3.14 x 5 x 15

=471 sq cm.

1. Find the volume of a cylindrical oil tank whose diametre is 8 cm and the height is 12 cm. Use π= 3.14

= 8/2

=4 cm.

Volume of the cylinder= πr2h

= 3.14 x (4×4) x 12

=3.14 x 16 x 12

=602.88 cube cm.

## FAQs

What is a cylinder?

Cylinders are three-dimensional geometric shapes with two parallel bases joined by a curved surface. The bases have a circular shape. This shape is found in everyday items such as pens, pencils, and cans.

How many types of cylinder there are?

There are four types of cylinder: Right Cylinder, Oblique Cylinder, Elliptical Cylinder, and Right Circular Hollow Cylinder.

What is the TSA and CSA of cylinders?

TSA means Total Surface Area of Cylinder.
CSA means Curved Surface Area of Cylinder or Lateral Surface Area.
The formula for TSA of cylinder= 2πr(h+r)
The formula for CSA of cylinder=  2πrh

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