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Cylinder: Shape, Formulas, Solved Examples

A cylinder is a three-dimensional geometric shape with two parallel, congruent circular bases connected by a curved surface. Explore the definition of a cylinder, its types, important formulas, and solved examples to understand its applications more effectively.

Chandni 8 Jan, 2025

Cylinder: Take a moment to look around, and you will notice cylinders everywhere. From candles and soda cans to water tanks and pipes, this geometrical shape is all around us.

A cylinder is a three-dimensional object with two parallel circular bases connected by a smooth, curved surface. The word "cylinder" comes from the Greek word "kylindros," which means "roller" or "barrel." This name reflects the rolling nature of a cylinder, a characteristic that matches its shape in geometry. Since a cylinder is a three-dimensional geometric shape, it has two key properties: surface area, which measures its outer covering, and volume, which calculates the space it occupies. cylinder shape

[video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Curious-Jr-Ad-3-1-1.mp4"][/video]

Cylinder Definition

A cylinder is a three-dimensional shape defined by two identical, parallel circular bases connected by a curved surface. The line segment connecting the centers of the two circular bases is called the axis, representing the height of the cylinder. The distance from the center of a circular base to its edge is called the radius, denoted as “r.” This cylindrical shape is a blend of two circles and a rectangle.

Cylinders are incredibly versatile and can be found in many objects around us. Examples include beverage cans, gas cylinders, drum barrels, batteries, telescope tubes, water bottles, and storage silos.

Number of Faces Vertices Edges in Cylinder

A cylinder is a geometrical shape with two flat circular faces and one curved surface. The two circular faces are identical in size and shape, positioned parallel to each other, one at the top and one at the bottom. These faces are connected by a curved surface, which looks like a rectangle rolled into a tube. If we think about its parts:

A cylinder has 3 faces.The two flat circular faces and the curved surface.
It has 2 edges. One edge at the top where the curved surface meets the upper circle and one edge at the bottom where it meets the lower circle.
It has 0 vertices because there are no sharp corners or points where edges meet.

This structure makes cylinders smooth and ideal for rolling when placed on their side.

Types of Cylinder

In geometry, cylinders are classified into four main types. These are as follows:

Right Circular Cylinder

This type has two parallel circular bases, and the axis (the line joining the centers of the bases) is perpendicular to the center of the bases. The bases are directly aligned, making it a regular and symmetrical shape. A common example is a soda can, which stands upright with perfectly aligned circular ends.

Oblique Cylinder

In an oblique cylinder, the sides are tilted, and the axis is not perpendicular to the bases. This means the top base is shifted sideways relative to the bottom base. The Leaning Tower of Pisa is a relatable example, as its tilted structure resembles the shape of an oblique cylinder.

Elliptic Cylinder

Unlike the right circular cylinder, the bases of an elliptic cylinder are shaped like ellipses instead of circles. This gives the cylinder a unique elongated or flattened appearance. Optical lenses are a practical example of this type of cylinder, commonly used in scientific instruments.

Right Circular Hollow Cylinder (Cylindrical Shell)

This type consists of two right circular cylinders, one inside the other, creating a hollow space between them. The axis of both cylinders is common and perpendicular to the bases, but the structure is different because of the hollow interior. Hydraulic cylinders, which are used in heavy machinery, are a typical example of this design. Right circular hollow cylinder (cylindrical shell)

Cylinder Formulas

Cylinders have formulas to calculate their volume , curved surface area (CSA) , and total surface area (TSA) . These formulas are useful for understanding how much space the cylinder occupies and how much surface it has. Let’s understand each of the cylinder formulas briefly below.

Volume of a Cylinder

The volume of a cylinder tells us how much space it occupies. Imagine a cylindrical container filled with oil; the volume will represent the total amount of oil it can hold. The volume of a cylinder is always measured in cubic units. V olume of a Cylinder Formula Volume (V) = πr ² h (cubic units)

r : Radius of the circular base.
h : Height of the cylinder (distance between the two bases).
π : It is constant, approximately equal to or

Curved Surface Area (CSA) of a Cylinder

The curved surface area (CSA), also called the lateral surface area, refers to the area of the cylinder's side, excluding the top and bottom bases. It’s like unrolling the curved part of a cylinder, similar to peeling off the label from a soda can or removing the outer layer of a roll of tape. T he curved surface area of a cylinder is always measured in square units

Curved Surface Area of Formula

CSA = 2πrh (square units)

r : Radius of the circular base
h : Height of the cylinder

Total Surface Area (TSA) of a Cylinder

The total surface area of a cylinder is the total area covering its outer surface. It includes three parts: the curved side surface and the two circular bases. Surface area is always measured in square units. Total Surface Area of a Cylinder Formula TSA = 2πr(h+r) (square units)

The term 2πrh is the curved surface area.
The term 2πr ² adds the areas of the two circular bases.

So, TSA combines the side surface and the top and bottom faces of the cylinder.

Cylinder Solved Examples

Example 1: Find the total surface area of a cylindrical drum with a radius of 5 feet and height of 10 feet in square feet.

Solution: Given: R = 5 feet, h = 10 feet

Formula:

TSA=2πr(h+r)

Substitute the values:

TSA=2π×5×(10+5) TSA=2π×5×15=150π square feet TSA≈150×3.14=471.00 square feet

Example 2: Find the curved surface area of a pillar with a radius of 4 cm and height of 9 cm.

Solution: Given: r=4 cm, h=9 cm

Formula:

CSA=2πrh

Substitute the values:

CSA=2 × 22/7 × 4 × 9 CSA=2 × 22 × 36 ÷ 7 CSA=2×22×36÷7 CSA≈226.29 square cm (rounded to two decimal places)

Example 3: Find the radius of a cylinder with a curved surface area of 352 sq. cm and height of 8 cm.

Solution: Given: CSA=352 sq. cm, h=8 cm

Formula:

CSA=2πrh

Substitute the values:

352 = 2 × 22/7 × r × 8 352 = 352/7 r r= 352/ (2×22×8÷7) =352 × 7/ 352 r=7 cms

Example 4: Find the total surface area of a cylinder if the curved surface area is 198 sq. cm, and the radius is 6 cm.

Solution: Given: CSA=198 sq. cm, r=6 cm

The formula for CSA:

CSA=2πrh

Find height (h):

198 = 2×22/7×6×h 198 = 264/7h h = 198 × 7/ 264 = 5.25

Now calculate TSA:

TSA=2πr(h+r) TSA=2×22/7×6×(5.25+6) TSA=2×22/7×6×11.25 TSA≈ 2 × 3.14 × 6 × 11.25 = 424.1 sq. cm (rounded to two decimal places)

Example 5: Find the volume of a cylindrical water tank with a radius of 7 feet and a height of 12 feet.

Solution: Given: r=7 feet, h=12 feet

Formula for volume:

Volume (V)=πr ² h

Substitute the values:

V=22/7 ×7 ² ×12 V=22/7 × 49 × 12 V=22×49×12÷7 V = 22 × 84 = 1848 cubic feet The volume of the water tank is approximately 1847.52 cubic feet.

Related Articles
Area of Rectangle	Isosceles Triangle
Composite Numbers	Differentiation
Perimeter of Rectangle	Surface Area of Cylinder

Cylinder FAQs

How is a cylinder different from a prism?

Both have parallel bases, but a cylinder has curved surfaces and circular bases, while a prism has flat surfaces and polygonal bases.

What happens to the surface area if the height of a cylinder is doubled?

When the height of a cylinder is doubled, the curved surface area increases proportionally, while the base areas remain unchanged. For example, a cylinder with a radius of 3 cm and a height of 5 cm has a curved surface area (CSA) of 2π(3)(5)=94.2 sq cm. . If the height is doubled to 10 cm, the CSA becomes 2π(3)(10)=188.4 sq cm. 2.. The CSA doubles, but the base areas stay the same.

How do engineers use cylinder formulas in real-life applications?

Engineers use TSA and CSA for material estimates and surface coatings, and volume for storage or capacity calculations in tanks and pipelines.

Can the CSA of a cylinder ever exceed its TSA?

No, because the TSA always includes the CSA plus the areas of the two bases.

Can a cylinder roll on its side?

Yes, a cylinder can roll on its side because of its smooth, curved surface, which allows it to move easily in a straight line when pushed or given momentum

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Cylinder: Take a moment to look around, and you will notice cylinders everywhere. From candles and soda cans to water tanks and pipes, this geometrical shape is all around us.

[video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Curious-Jr-Ad-3-1-1.mp4"][/video]

Cylinder Definition

Number of Faces Vertices Edges in Cylinder

A cylinder has 3 faces.The two flat circular faces and the curved surface.
It has 2 edges. One edge at the top where the curved surface meets the upper circle and one edge at the bottom where it meets the lower circle.
It has 0 vertices because there are no sharp corners or points where edges meet.

This structure makes cylinders smooth and ideal for rolling when placed on their side.

Types of Cylinder

In geometry, cylinders are classified into four main types. These are as follows:

Right Circular Cylinder

Oblique Cylinder

Elliptic Cylinder

Right Circular Hollow Cylinder (Cylindrical Shell)

Cylinder Formulas

Volume of a Cylinder

r : Radius of the circular base.
h : Height of the cylinder (distance between the two bases).
π : It is constant, approximately equal to or

Curved Surface Area (CSA) of a Cylinder

Curved Surface Area of Formula

CSA = 2πrh (square units)

r : Radius of the circular base
h : Height of the cylinder

Total Surface Area (TSA) of a Cylinder

The term 2πrh is the curved surface area.
The term 2πr ² adds the areas of the two circular bases.

So, TSA combines the side surface and the top and bottom faces of the cylinder.

Cylinder Solved Examples

Example 1: Find the total surface area of a cylindrical drum with a radius of 5 feet and height of 10 feet in square feet.

Solution: Given: R = 5 feet, h = 10 feet

Formula:

TSA=2πr(h+r)

Substitute the values:

TSA=2π×5×(10+5) TSA=2π×5×15=150π square feet TSA≈150×3.14=471.00 square feet

Example 2: Find the curved surface area of a pillar with a radius of 4 cm and height of 9 cm.

Solution: Given: r=4 cm, h=9 cm

Formula:

CSA=2πrh

Substitute the values:

CSA=2 × 22/7 × 4 × 9 CSA=2 × 22 × 36 ÷ 7 CSA=2×22×36÷7 CSA≈226.29 square cm (rounded to two decimal places)

Example 3: Find the radius of a cylinder with a curved surface area of 352 sq. cm and height of 8 cm.

Solution: Given: CSA=352 sq. cm, h=8 cm

Formula:

CSA=2πrh

Substitute the values:

352 = 2 × 22/7 × r × 8 352 = 352/7 r r= 352/ (2×22×8÷7) =352 × 7/ 352 r=7 cms

Example 4: Find the total surface area of a cylinder if the curved surface area is 198 sq. cm, and the radius is 6 cm.

Solution: Given: CSA=198 sq. cm, r=6 cm

The formula for CSA:

CSA=2πrh

Find height (h):

198 = 2×22/7×6×h 198 = 264/7h h = 198 × 7/ 264 = 5.25

Now calculate TSA:

TSA=2πr(h+r) TSA=2×22/7×6×(5.25+6) TSA=2×22/7×6×11.25 TSA≈ 2 × 3.14 × 6 × 11.25 = 424.1 sq. cm (rounded to two decimal places)

Example 5: Find the volume of a cylindrical water tank with a radius of 7 feet and a height of 12 feet.

Solution: Given: r=7 feet, h=12 feet

Formula for volume:

Volume (V)=πr ² h

Substitute the values:

V=22/7 ×7 ² ×12 V=22/7 × 49 × 12 V=22×49×12÷7 V = 22 × 84 = 1848 cubic feet The volume of the water tank is approximately 1847.52 cubic feet.

Related Articles
Area of Rectangle	Isosceles Triangle
Composite Numbers	Differentiation
Perimeter of Rectangle	Surface Area of Cylinder