Cylinder Formula

The cylindrical shape is one of the most common shapes that we see everywhere in our daily life. Moreover, our household gas cylinder, pillars, wires, cables, bottles, coins, etc. are all in a cylindrical shape. Furthermore, it is an important shape because of its strength and durability and they require very his pressure to get destroyed. Learn cylinder formula below.

Cylinder

It refers to a 3D (3 dimensional) shape that has two flat round bases (one at the top and one at the bottom) and one curved side. In addition, it has a curved surface in the middle. Moreover, the base and the top flat surfaces are alike. It also means that the bases are always parallel and congruent to each other. Furthermore, it has two vertices.

Types of Cylinder

Basically, we can find cylinders in two basic shapes namely right and oblique.

Right Cylinder

It is the type of cylinder in which the two bases of the cylinder are exactly over each other and the axis of the right angle of the base, then such cylinder is known as a right cylinder. For example, tin cans, coins, LPG cylinders, etc.

Oblique Cylinder

In this type of cylinder the two bases are not symmetrical to each other. Also, the two bases are sideways and the axis is not a right angle to the base. These type of cylinders are called oblique cylinder. For example, pillars, etc.

Besides, the calculation method of both the cylinder is the same.

Cylinder Formula

There are two formulas important for a cylinder in consideration.

First, is the surface area formula and second is the volume formula. Now, let’s discuss them in detail

Download Cylinder Formula Cheat Sheet Below

Surface area Formula

As we discussed earlier the surface of the cylinder has two round bases and a curved side. Firstly, on observing the figure we find that there are two circles and a rectangle. Moreover, one of the circle lies at the top and one at the bottom of the cylinder. Also, both circles are of the same size. Besides, the curved surface of the rectangle is the rectangle. Now let’s figure out the formula.

The figure has two round circles one at the top and one at the bottom. Furthermore, the area of one circle is \(\pi r^{2}\). So, the area of two circles will be\(2\pi r^{2}\).

Most noteworthy, the radius of the cylinder will be the same as the radius of the base and top that is ‘r’. So, the areas of the rectangle = length × breadth and the circumference of the circle are \(2 \pi r\) and its height is h. Then, the area of the curved surface will be =\(2 \pi r\) × h = \(2 \pi r h\).

Now, the area of the cylinder will be = \(2\pi r^{2}\) + \(2 \pi r h\)

OR

The total surface area of the cylinder will be = \( 2 \pi r\) (r + h)

Derivation of the Formula

\(2\pi\) = refers to the values of the circle in pi
r = refers to the radius of the cylinder
h = is the height of the cylinder

The volume of a cylinder

The volume of the cylinder is

V = \(\pi r^{2}\)

Derivation

V = refers to the volume of the cylinder is \(m^{3}\)
\(\pi\) = refers to the value of pie
r = refers to the radius of the cylinder
h = is the height of the cylinder

Solved Example on Cylinder Formula 

Suppose there is a cylinder of height 7 cm and radius of 6 cm. Calculate its total surface area?

Solution:

Surface area = \( 2 \pi r\) (r + h)
A = \( 2 \pi × 6\) (6 + 7)
A = 2 × 3.14 × 6 (13)
A = 37.68 × 13
A = 490.1

The surface area of the cylinder is 490.1 cm.