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

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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.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If $OP = 13$ cm, then find the length AB and PA.
View Solution
2.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$
View Solution
3.
$ABCD$ is a parallelogram such that $AF = 7 \text{ cm}$, $FB = 3 \text{ cm}$ and $EF = 4 \text{ cm}$, length $FD$ equals
- $\frac{21}{4} \text{ cm}$
- $\frac{28}{3} \text{ cm}$
- $\frac{12}{7} \text{ cm}$
- $5.5 \text{ cm}$
View Solution
4.
In the figure given above, $\triangle ABC \sim \triangle XYZ$, then find the values of $x$ and $y$.
View Solution
5.
The first term of an AP is $p$ and the common difference is $q$, then its 10th term is :
- $q - 9p$
- $p - 9q$
- $p + 9q$
- $2p + 9q$
View Solution
6.
Assertion (A) : H.C.F. $(36 m^{2}, 18 m) = 18 m$, where $m$ is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
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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.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.

2.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

3.
\(ABCD\) is a parallelogram such that \(AF = 7 \text{ cm}\), \(FB = 3 \text{ cm}\) and \(EF = 4 \text{ cm}\), length \(FD\) equals

4.
In the figure given above, \(\triangle ABC \sim \triangle XYZ\), then find the values of \(x\) and \(y\).

5.
The first term of an AP is $p$ and the common difference is $q$, then its 10th term is :

6.
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

Comments

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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.PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.

2.Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

3.\(ABCD\) is a parallelogram such that \(AF = 7 \text{ cm}\), \(FB = 3 \text{ cm}\) and \(EF = 4 \text{ cm}\), length \(FD\) equals

4.In the figure given above, \(\triangle ABC \sim \triangle XYZ\), then find the values of \(x\) and \(y\).

5.The first term of an AP is $p$ and the common difference is $q$, then its 10th term is :

6.Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number. Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.

2.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

3.
\(ABCD\) is a parallelogram such that \(AF = 7 \text{ cm}\), \(FB = 3 \text{ cm}\) and \(EF = 4 \text{ cm}\), length \(FD\) equals

4.
In the figure given above, \(\triangle ABC \sim \triangle XYZ\), then find the values of \(x\) and \(y\).

5.
The first term of an AP is $p$ and the common difference is $q$, then its 10th term is :

6.
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.