# Cylinder

A cylinder is a three-dimensional solid consisting of two parallel circular bases joined together by a curved surface at a particular distance from the center of the circular bases.

The center of the two bases is joined by a line segment, called the axis. The perpendicular distance between the bases is the height or altitude (h) and the distance from the axis to the outer surface is its radius (r).

The top view of the cylinder looks like a circle and the side view looks like a rectangle. Unlike other 3-D shapes such as a cone, cube, or a cuboid, a cylinder does not have vertices since it has two circular faces and no straight lines. Thus, a cylinder is a combination of two circles and a rectangle. It is similar to a prism, since they have the same cross-section everywhere.

## Properties

1. Has 2 curved edges, 1 curved surface, and 2 flat faces
2. Has 2 identical, circular bases that are parallel and congruent
3. The size depends on the radius and the height of the cylinder

## Types

In geometry, cylinders can be of 4 types. They are named and described below:

### 1) Right Cylinder

A right cylinder is a cylinder having its axis perpendicular (forming right angle) to the plane of its 2 bases. If its 2 bases are circular is called the right circular cylinder.

### 2) Oblique Cylinder

An oblique cylinder is a cylinder with its axis not perpendicular to the plane of its 2 bases. Thus, if a cylinder is not right circular it will be an oblique cylinder.

### 3) Elliptic Cylinder

An elliptical cylinder is a cylinder with bases in the form of an ellipse.

### 4) Right Circular Hollow Cylinder

A right circular hollow cylinder is a cylinder that consists of two right circular cylinders bounded one inside the other.

## Formulas

### Volume

The volume of the cylinder is the space occupied by it in any 3-dimensional plane. It determines its density or the amount of space it occupies. It is expressed in cubic units such as m3, cm3, and mm3. The formula to calculate the volume is given below:

Volume (V) = Ï€r2h, here Ï€ = 22/7 = 3.141, r = radius, h = height

Let us solve an example to understand the concept better.

Calculate the volume of the cylinder with a radius of 7 units and a height of 10 units.

Solution:

As we know,
Volume (V) = Ï€r2h, here Ï€ = 3.141, r = 7 units, h = 10 units
= 3.141 Ã— (7)2 Ã— 10
= 1539.09 cubic units

### Surface Area

A cylinder has 2 types of surface areas. It is expressed in square units such as m2, cm2, and mm2.

#### Lateral (Curved) Surface Area

The lateral or the curved surface area (CSA) of a cylinder is the area formed by the curved surface of the cylinder. It is thus the space occupied between the two parallel circular bases. The formula to calculate CSA is given below:

Curved Surface Area (CSA) = 2Ï€rh, here Ï€ = 22/7 = 3.141, r = radius, h = height

Let us solve an example to understand the concept better.

Solution:

As we know,

Curved Surface Area (CSA) = 2Ï€rh, here Ï€ = 3.141, r = 6 inches, h = 18 inches

= 2 Ã— 3.141 Ã— 6 Ã— 18

= 678.5 in2

#### Total Surface Area

The total surface area (TSA) of a cylinder is the sum of the curved surface area and the area of two circular bases. The formula to calculate TSA is given below:

Total Surface Area (TSA) = 2Ï€r(r + h), here Ï€ = 22/7 = 3.141, r = radius, h = height

Let us solve an example to understand the concept better.

Find the total surface area of a cylinder with a base radius of 3 inches and a height of 8 inches.

Solution:

As we know,
Total Surface Area (TSA) = 2Ï€r(r + h), here Ï€ = 3.141, r = 3 inches, h = 8 inches
= 2Ã— 3.141 Ã— 3(3 + 8)
= 2Ã— 3.141 Ã— 33
= 207.3 in2

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