In view of the coronavirus pandemic, we are making LIVE CLASSES and VIDEO CLASSES completely FREE to prevent interruption in studies
Home > Formulas > Maths Formulas > Surface Area of Cylinder Formula
Maths Formulas

Surface Area of Cylinder Formula

A cylinder is a three-dimensional figure with two round flat bases and one curved side. In other words, a closed solid has two parallel circular bases connected by a curved surface. It has no vertices. Let us now discuss the surface area of cylinder formula.

Lateral or Curved Surface Area of Cylinder Formula

A cylinder is a rectangle with two circular bases. The faces of the cylinder are parallel and congruent circles. The cylinder has one curved surface. The height of the cylinder is the perpendicular distance between the base.

The lateral surface of an object is defined as the area of a curved surface, excluding the area of its base and top. In the lateral surface area of a cylinder, the radius is directly proportional to the height of the Cylinder.

The Curved Surface Area of the Cylinder = \(2 \pi r h\)

Where,

\(\pi\) Pi, approximately 3.142
r the radius of the cylinder
h height of the cylinder

Total Surface Area of Cylinder Formula

The surface area of the cylinder is the area of a curved surface of a cylinder including circular top and base.

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

Where,

\(\pi\) Pi, approximately 3.142
r the radius of the cylinder
h height of the cylinder

Surface Area of Cylinder FormulaDerivation of Surface Area of Cylinder Formula

Curved Surface Area

Take a rectangle and roll it up, you end up with a cylinder. Therefore, if you want to compute the curved surface area of a cylinder, imagine unrolling it. The area of the rectangle is the width multiplied by the height. Here, the width of the rectangle is the height h of the cylinder, and the length of the rectangle is the circumference of the circle is 2 \pi r.

\(Area of rectangle = l × b = 2 \pi r  ×  h\)

\(The Curved Surface Area of the Cylinder = 2 \pi r h\)

Total Surface Area of a Cylinder

  • Area of each circle can be found from the radius r of the circle. The area of a circle is \pi r2, so the combined area of the two circles is 2 \pi r2.
  • The area of the rectangle is the breadth times height. The breadth of the rectangle is the height h of the cylinder, and the length of the rectangle is the distance around the end circles. This is the circumference of the circle is 2 \pi r. Thus, the rectangle area is 2 \pi r  ×  h.

Combining these parts, we get the final formula:

Area = 2 π r2 + 2 π r h

By factoring 2 π r from each term, we can simplify this to

Area = 2 π r (r + h)

Solved Examples

Q.1. Find the curved surface area of a cylinder of height 6 cm and the radius is 2 cm.

Solution: h = 6 cm; r= 2 cm

Area = 2 π r h
= 2 × 3.14 × 2  × 6
= 75.36 cm2

Q.2. Find the total surface area of a cylindrical tin of radius 17 cm and height 3 cm.

Solution: Radius r = 3 cm,  Height h = 17 cm

Total surface area of tin = 2 π r (r + h)
= 2 × 3.14 × 3 (3 + 17)
= 18.84 × 20
= 376.2 cm2

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
tutor
tutor
Ashhar Firdausi
IIT Roorkee
Biology
tutor
tutor
Dr. Nazma Shaik
VTU
Chemistry
tutor
tutor
Gaurav Tiwari
APJAKTU
Physics
Get Started

Leave a Reply

avatar
  Subscribe  
Notify of

Stuck with a

Question Mark?

Have a doubt at 3 am? Our experts are available 24x7. Connect with a tutor instantly and get your concepts cleared in less than 3 steps.
toppr Code

chance to win a

study tour
to ISRO

Download the App

Watch lectures, practise questions and take tests on the go.

Get Question Papers of Last 10 Years

Which class are you in?
No thanks.