 # Cylinder

Cylinder is a three-dimensional solid shape.Out of many basic shapes in Geometry, Cylinder is the one having  two parallel bases which are circular in shape and at a distance from each other which is called as its height. It has its own surface area and volume. The total surface area of a Cylinder is based on two main factors:

• Base of a Cylinder is a Circle.

• The distance between two bases(axis) of a Cylinder is Height, H.

• The length from an axis to the outer ring of the circular base is called Radius R.

### Important Cylinder Formulas

Using the three main factors of a Cylinder, we get the three important formulas of Cylinder.

1. Total Surface Area of Cylinder

2. Lateral surface Area of Cylinder

3. Volume of Cylinder

1. Total Surface Area of Cylinder - The Total Surface Area of a Cylinder is the area which covers the space between the two parallel circular bases(Curved surface area) and the area of the two bases(Area of Circles).

 Total Surface Area of a Circle = 2πrh + 2πr2 = 2πr(h+r) square units, where h is the height or distance between the two axis and r is the radius from the axis to the outer boundary of the circle.

2. Curved Surface Area

The area of the space covered between the two circular bases in the cylinder is called the Curved Surface Area or Lateral Surface Area of a Cylinder.

 Curved Surface Area, C.S.A = 2πrh square units, where r is the radius of the two circular bases and h is the height of the distance between the two circular bases.

3.Volume of a Cylinder: The space inside any three dimensional object is known as its volume. In a simpler way, the total amount of water which can be stored in a cylinder is its volume.

 Volume of a Cylinder, V = πr2h cubic units, where h is the height of the cylinder and r is the radius of the circular base of the cylinder.

What are the Properties of a Cylinder?

There are many important properties of Cylinder. Few of them are given below.

1. The two circular bases of a Cylinder are always parallel and congruent.

2. A right cylinder is formed when the axis forms a right angle with the bases of the cylinder which are opposite to each other.

3. Similarity between a prism and a cylinder is that both have the same cross section at each point.

4. Contrary to the Right Cylinder, if the two bases of the cylinder are not over each other and the axis do not make a right angle with the two bases, that cylinder would be considered as the Oblique Cylinder.

5. The cylinders which have circular bases are known as circular cylinders and cylinders having elliptical bases are known as Elliptical Cylinders.

Real Life Examples of Cylinder

• Pipe

• Water Tank

• LPG Cylinder

• Batteries

• Water Glass

• Test Tube etc

### Problems

Question 1: If the height of the cylinder is 10 cm, and radius is 7cm, Find it’s Total surface area?

Solution: The total surface area of the cylinder is equal to 2πr(r+h) square units

It is given that r = 5 cm and h = 10 cm.

So, the total surface area of the Cylinder is 2 * 22/7 * 7* (7 + 10) = 2 * 22 * 17 = 748 cm2

Question 2: Find the volume of the cylinder having height 6 cm and diameter 10cm?

Solution: The volume of a cylinder is its capacity to contain the water in it.

Given, r = 5cm (d/2) as d= 10cm

The formula to find the volume of the Cylinder is πr2h = 3.14 * 5 *5 * 6 = 471 cm3

1. What is the Shape of a Cylinder?

Ans: Cylinder shape has two circles at the base which are at a particular distance from each other called as Height. A tube will be the best example to define its shape.

2. What is Cylinder in Maths?

Ans: It is a 3-dimensional figure having two circular bases connected with an axis. It looks like a LPG cylinder.

3. How do you Solve a Cylinder?

Ans: To solve the cylinder, we use the formula, πr2h, where r is the radius of the two circular bases and h is the height of the axis joining them.

4. What are the Properties of Cylinders?

Ans: It is a three dimensional figure.

It has two circular bases connected with an axis known as height

• 5. What is the Formula of Cylinder?

Ans: The formula for Cylinder is, TSA = 2πr(r+h)