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Cylinder

A Cylinder is a solid with circular base. It can be of the shape of a pillar, a rubber tube, the trunk of a tree, etc. The term circular cylinder is used to describe a right circular cylinder. A circular cylinder  having perpendicular base and height is known as a right circular cylinder.

The diagram given here is of a right circular cylinder:

Right Circular Cylinder

In the above diagram, h = height of the circular cylinder

r = radius of base of circular cylinder

We can also say that a circular cylinder is a rolled form of a rectangle. The area of the rectangle that forms the shape of a cylinder is called the curved surface area of a cylinder, since the rectangle forms the curved surface of the cylinder.How?
 
It is explained here in the given figure:

Rolling of Cylinder


When we cut a cylinder vertically, the cross section obtained is a rectangle. In other words, when a rectangle is revolved around one of its sides, a cylinder is obtained.

Cross Section of Cylinder

When we add the area of the top and bottom circles of a cylinder to its curved surface area, we get the total surface area of a cylinder.

Related Calculators
Cylinder Calculator Volume a Cylinder
Area Cylinder Calculator
 

Cylinder Definition

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The solid enclosed by the surface and by two planes perpendicular to the axis is called as a cylinder. A cylinder is a closed three dimensional solid which is made up of two parallel circular bases connected by a curved surface.

The bases are always congruent to each other:

Cylinder Shape:


Cylinder
In this figure: r is the radius of a cylinder and h is the height of a cylinder which is perpendicular distance between the bases.

Cylinder Volume

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The amount of space occupied by the cylinder is its volume. The volume of a cylinder is the area of its circular base times its height. Volume of cylinder is measured in cubic units.

Cylinder Volume Formula:


Formula for volume of a cylinder = $\pi$r$^2$h

where, r:  Radius of a cylinder

h: Height of a cylinder

and $\pi$ is equal to $\frac{22}{7}$ or 3.14

Curved Surface Area of a Cylinder

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A cylinder is a solid with two congruent, parallel bases. These bases are connected by a rounded surface. A right circular cylinder with circular bases that are directly above and below each other.

The volume of a cylinder is obtained by multiplying the area of the base by height. The volume of a cylinder is given by V = $\pi$ r$^2$ h where v is volume, r is the radius and h is the height.

The curved surface area of a cylinder is given by the following formula,

Curved Surface Area = 2 * $\pi$ * r * h

where, r = radius of the base circles of cylinder

h = height of the cylinder

Cylinder Surface Area

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Surface area of a cylinder is the sum of curved surface area and area of each base of the cylinder.

Total Surface Area = Curved surface area + Area of top + Area of bottom

= 2 $\pi$ r h + $\pi$ r$^2$ + $\pi$ r$^2$ ($\because$ Top and bottom of a cylinder are circular)

= 2$\pi$r(r + h)

Cylinder Formula:

Cylinder area = 2$\pi$r(r + h)

where, r = Radius of a cylinder

h = Height of a cylinder
A surface generated by a line which intersects a fixed circle and is perpendicular to the plane of the circle is the right cylinder. The normal to the plane of the circle through its center is the axis of the cylinder.A right circular cylinder is a cylinder whose bases are perpendicular to the axis.
Differences of Right Circular & Oblique Cylinder

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Solved Examples on Cylinders

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Given below are some of the examples on Cylinder

Solved Examples

Question 1: Find the curved surface area of the cylinder with height 15 cm and radius of base circle 5 cm.
Solution:

Given, Radius (r) = 5 cm

Height (h) = 15 cm

Area of curved surface, CSA = 2 $\pi$ r h

= 2 $\times$ 3.14  $\times$ $\times$ 15

= 471
The curved surface area of the cylinder is 471
cm2



Question 2: Find the Total Surface Area of a cylinder whose height is 20 meters and radius of base circle is 2 meters.
Solution:

Given, Radius (r) = 2 m

Height (h) = 20 m

Total Surface Area of Cylinder, TSA = 2$\pi$ r$^2$ + 2 $\pi$ r  h

= 2 $\times$ 3.14 $\times$ 4 + 2 $\times$ 3.14 $\times$ 2 $\times$ 20

= 25.12 + 251.2

= 276.32

Total Surface Area of a cylinder is 276.32 m3



Question 3: Find the Volume of a cylinder whose height is 28 cm and diameter is 12 cm
Solution:

Given, Diameter of a cylinder = 12 cm, therefore Radius = $\frac{\text{Diameter}}{2}$ = $\frac{12}{2}$ = 6

Radius (r) = 6 cm

Height (h) = 28 cm

Volume = $\pi$ r$^2$ h

= 3.14 * 36 * 28

= 3165.12

$\therefore$ Volume of a cylinder is 3165.12 cm3



More topics in Cylinder
Surface Area of Cylinder Volume of Cylinder
Right Circular Cylinder
NCERT Solutions
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