Surface Area of Cylinder: Formula, CSA and TSA of Cylinder

Content Curator

The Surface Area of Cylinder can be divided into two categories: The Curved Surface Area (CSA) and the Total Surface Area (TSA). The area of any shape in geometry is the area it covers in a plane. A cylinder has two sorts of surfaces: one with a curved surface and another with two circular bases. Both circular bases have the same area.

Table of Content

Surface Area of Cylinder
Formula of Surface Area of Cylinder
Curved Surface Area of Cylinder
Base Area of Cylinder
Total Surface Area of Cylinder
Things to Remember
Important Questions

Read Also: Pythagoras Theorem

Surface Area of Cylinder

The total area covered by a cylinder in three-dimensional space is called the surface area of the cylinder.

The area of a cylinder is equal to the sum of the areas of two circular bases and the area of a curved surface.
The two circular bases of the right cylinders are perfectly aligned, and the axis line forms a right angle to the base.
The oblique cylinder is formed when one of the circular bases is moved and the axis does not generate a right angle to the base.
The lateral surface is another name for this curved surface.
Radius, height, axis, base, and side are some of the characteristics needed to compute the cylinder area.
The radius of the cylinder is equal to the radius of the circular base.
The height of the cylinder is determined by measuring the perpendicular distance between two circular bases, and the axis is the line that connects the base's center.

Surface Area of Cylinder

Read More: Surface Area of a Cone Formula

The video below explains this:

Surface Area and Volume Detailed Video Explanation:

Formula of Surface Area of Cylinder

The surface area of a cylinder is equal to the sum of the curved surface and the area of the cylinder's two circular bases.

Surface Area of Cylinder = Curved Surface + Area of Circular bases

Surface Area of Cylinder= 2πr (h + r) sq. unit

Where,

π (Pi) = 3.142 or = 22/7

r is the radius of the cylinder

h height of the cylinder.

Also Read:

Surface Area and Volume Force

Surface Area of Hemisphere

Curved Surface Area of Cylinder

The curved surface area of a cylinder, or the area obtained by omitting the area of its two circular bases, is called the curved surface area. It is also referred to as the lateral surface area (LSA).

The CSA of a cylinder with a base radius of ‘r' and a height of ‘h' is calculated as follows:

Curved surface area (CSA) of cylinder = 2πrh sq. units.

Curved surface area of cylinder

Read More: Independent Events

Base Area of Cylinder

The base area of the cylinder has a round form. As a result, we can conclude from the formula for the area of a circle that-

Area of the circular bases of cylinder = 2 (πr²) (because the cylinder has two circular bases)

Area of the circular face of cylinder

Read Further: Bayes Theorem Formula

Total Surface Area of Cylinder

The total surface area of a cylinder is equal to the sum of its faces. The sum of the curved and circular areas of the cylinder equals the total surface area with radius ‘r' and height ‘h'.

Total surface area (TSA) = 2π × r × h + 2πr² = 2πr (h + r) sq. units

Total Surface Area of Cylinder

Read Also: Geometry Formula

Things to Remember Based on Surface Area of a Cylinder

Surface Area of Cylinder (in terms of π) = 2πr (h + r) sq. unit
Curved surface area (CSA) of cylinder = 2πrh sq. units.
Area of the circular bases of cylinder = 2 (πr²)
Total surface area (TSA) = 2π × r × h + 2πr²= 2πr (h + r) sq. units

Also Check:

Surface Area of a Cylinder

Surface Area of Hollow Cylinder

Important Questions Based on Surface Area of a Cylinder

Ques: What is the formula of curved surface area and base area of a cylinder? (1 Mark)

Ans: The formula of the curved surface area of the cylinder is 2πrh sq. units.

The formula for the base area of the cylinder is 2 (πr²) sq. units.

Ques: What is a cylinder and how is its total surface area calculated? (1 Mark)

Ans: A cylinder is a three-dimensional solid and one of the most fundamental curvilinear geometric shapes. The formula to calculate its total surface area is 2πr (h + r) sq. units

Ques: Calculate the cost required to paint a container that is in the shape of a right circular cylinder. Given a base radius of 14 m and a height of 25 m, the painting cost is INR 6/m2. (Take π = 22/7) (2 Marks)

Ans: Total surface area = 2πr (h + r)

Total surface area = 2 x 22/7 x 14 (25+14)

Total surface area = 2 x 22/7 x 14 x 39

Total surface area = 3432 sq. m

Total cost of painting the container = 6 x 3432= Rs. 20592.

Also Read:

Congurence of Triangles

Triangles

Ques: Given the height of the cylinder- 9 m; diameter- 8m; painting cost is INR 5/m2. (Take π = 22/7). Calculate the total cost and total surface area of the cylinder. (2 Marks)

Ans: Total Surface Area= 2πr (h + r)

r= 8/2 = 4m.

Total Surface Area= 2πr (h + r)

Total Surface Area= 2 x 22/7 x 4 x (9 + 4)

Total Surface Area= 2 x 22/7 x 4x 13

Total Surface Area = 326.85 sq. m

Total Cost = 5 x 326.85 = INR 1634.25

Ques: Given, the surface area of the cylinder is 345π sq. m; radius- 5m. Find the height of the cylinder. (2 Marks)

Ans: Surface area of the cylinder = Area of the cylinder

345π = 2πr (h + r)

345 x 3.14 = 2x3.14x5 (h + 5)

1083.3= 31.4 (h+5)

(h + 5)= 34.5

h= 34.5 – 5

h= 29.5m

Mathematics Related Links:

Three-Dimensional Geometry Introduction	Section Formula
Negative of a Vector	Area Between a Line and a Plane
Linear Programming	Conditional Probability

CBSE X Related Questions

1.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.
View Solution
2.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.
View Solution
3.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
View Solution
4.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.
View Solution
5.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is
- $\frac{5}{12}$
- $\frac{5}{6}$
- $1$
- $0$
View Solution
6.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is
- $50^\circ$
- $60^\circ$
- $45^\circ$
- $30^\circ$
View Solution

View All

CBSE X Syllabus

Mathematics Preparation Guides

Arithmetic Progressions: Properties, Formulas and Solved Examples

Distance Formula and Derivation of Coordinate Geometry

Probability- A Theoretical Approach: An Overview and Examples

Area of Circle: Area Formula, Derivation with Solved Examples

Mode of Grouped Data

Pythagoras Theorem: Formula, Theorem, Proof and Examples

Nature of Roots of Quadratic Equation

Probability: Concepts, Problems and Solved Examples

Trigonometry: Ratios, Identities & Trigonometric Table

Heights and Distances: Applications in Trigonometry

Real Numbers: Euclid’s Division Lemma, Properties & Sets

Surface Areas and Volumes Revision Notes

Circles: Definition, Properties, Parts, Theorems

Constructions Revision Notes

Pair of Linear Equations In Two Variables Important Questions

Circles Revision Notes: Theorems of Tangent to the Circle

Statistics Important Questions

Mathematics NCERT Solutions

Euclid's Division Lemma: Proof, Finding HCF & Examples

Area of a Sector: Definition, Formulae and Solved Examples

Real Numbers: Definition, Properties and Examples

Events in Probability: Definition, Types, Examples

Relation Between HCF and LCM: Definition, Methods and Formulas

Geometric Probability: Formula, Illustration, Model

Algebra Formula: Important Formulas in Algebra & Solved Examples

Angle of Depression: Definition, Formula and Solved Examples

Cyclic Quadrilateral: Properties, Theorems and Formulas

Polynomial Notation: Types, Remainder Theorem, Linear and Quadratic Equation

Surface Area of Cylinder: Formula, CSA and TSA of Cylinder

Surface Area of Cylinder

Surface Area and Volume Detailed Video Explanation:

Formula of Surface Area of Cylinder

Curved Surface Area of Cylinder

Base Area of Cylinder

Total Surface Area of Cylinder

Things to Remember Based on Surface Area of a Cylinder

Important Questions Based on Surface Area of a Cylinder

CBSE X Related Questions

1.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

2.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

3.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

4.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

5.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

6.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

Comments

SUBSCRIBE TO OUR NEWS LETTER

Surface Area of Cylinder: Formula, CSA and TSA of Cylinder

Surface Area of Cylinder

Surface Area and Volume Detailed Video Explanation:

Formula of Surface Area of Cylinder

Curved Surface Area of Cylinder

Base Area of Cylinder

Total Surface Area of Cylinder

Things to Remember Based on Surface Area of a Cylinder

Important Questions Based on Surface Area of a Cylinder

CBSE X Related Questions

1.A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

2.The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

3.Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

4.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

5.Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

6.An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

2.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

3.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

4.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

5.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

6.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is