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:**

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:**

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.

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.

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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:

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.

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

### 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.**

→ Read More### Solved Examples

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

** Solution: **

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

** Solution: **

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

** Solution: **

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.

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.

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

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

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)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.

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Given below are some of the examples on Cylinder

Given, Radius (r) = 5 cm

Height (h) = 15 cm

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

= 2 $\times$ 3.14 $\times$ 5 $\times$ 15

= 471

The curved surface area of the cylinder is 471 cm^{2}

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 m^{3}

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 cm^{3}

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Surface Area of Cylinder | Volume of Cylinder |

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