Volume of a Cylinder - How to Find Volume of Cylinder?

Volume of a Cylinder

The volume of a cylinder measures the space inside it. In simple words, it tells us how much the cylinder can hold, which we call its capacity. For example, if the cylinder serves as a water tank, its volume shows the number of litres of water it can store. We calculate this capacity using the formula πr²h. Here r represents the radius of the circular base, h represents the height of the cylinder, and π is approximately 3.141.

What is a Cylinder?

A cylinder is a three-dimensional geometric shape that has two parallel and identical circular bases connected by a smooth, curved surface. The straight line joining the centers of these two circular bases is known as the axis of the cylinder. If this axis meets the bases at a right angle, the cylinder is called a right cylinder.

Types of Cylinders

Understanding the different types of cylinders is important because the method used to calculate volume can vary slightly depending on the type.

1. Right Circular Cylinder: The most common type, where the bases are perfect circles and the axis is perpendicular to the bases.

2. Oblique Cylinder: A cylinder in which the axis is not perpendicular to the bases. The sides lean at an angle.

3. Elliptic Cylinder: The bases of the cylinder are ellipses instead of circles.

4. Hollow Cylinder: A cylinder that is empty on the inside, formed by two concentric cylinder

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Volume of Cylinder Formula

A right circular cylinder has a circular base. The area of the base is  π × r². So, to find the cylinder’s volume, we multiply this area by its height.

Volume of cylinder formula = πr2h

Where:

• π  is a mathematical constant, approximately 3.14159 or 22/7

• r is the radius of the circular base

• h is the height of the cylinder

This formula works for both solid and liquid materials and is used in countless industries to calculate cylinder volume.

Read more: Volume - Formula, Definition, Calculate, Examples

Units for Measuring the Volume of a Cylinder

The volume of a cylinder is always measured in cubic units because it represents the amount of space inside a three-dimensional shape.

Common Cubic Units:

• mm³ – cubic millimetres, used for very small cylinders

• cm³ – cubic centimetres, used in most school-level problems

• m³ – cubic metres, used for large cylinders like tanks or silos

• in³ – cubic inches, commonly used in some international systems

• ft³ – cubic feet, often used in construction or storage

Capacity Units (for liquids):

• 1 cm³ = 1 millilitre (mL)

• 1,000 cm³ = 1 litre (L)

• 1 m³ = 1,000 litres (L)

These units help measure how much material or liquid a cylinder can hold. The correct unit depends on the size of the object and the context of the problem.

Read More: Surface Area of Cylinder

Steps to Calculate Cylinder Volume

Follow the steps below to calculate  the cylinder volume:

Step 1: Measure the Radius: If only the diameter is given, divide it by 2 to find the radius.

Step 2: Measure the Height: Ensure that the height and radius are in the same unit.

Step 3: Apply the Formula: V =  πr2h

Step 4: Use an Approximate Value for Pi: Use either 3.1416 or 22/7, depending on the requirement.

Step 5: Include Units: The volume will be expressed in cubic units, such as cm³, m³, or in³.

Volume of a Cylinder Calculator

Many people prefer using tools like a volume of a cylinder calculator to simplify the process, especially in professional settings or during exams.

A volume of a cylinder calculator asks for:

• Radius (or diameter)

• Height

• Optionally, choice of unit (cm, m, in)

After entering the values, it instantly returns the volume in the correct unit. 

Volume of a Hollow Cylinder

A hollow cylinder is a cylinder with a hollow center, much like a pipe or tube. It has two circular bases:

• The outer circle with radius r₁

• The inner circle with radius r₂

• The height of the cylinder is h

To find how much space is inside the hollow part, subtract the volume of the inner (empty) cylinder from the volume of the outer (solid) cylinder.

Formula: V = π × h × (r₁² − r₂²) 

Here, V represents the volume of the material forming the hollow cylinder.

Volume of Elliptic Cylinder 

If the base is an ellipse, the formula changes slightly.

V = πabh

Where a and b are the semi-major and semi-minor axes of the elliptical base.

Volume of Oblique Cylinder 

The volume of an oblique cylinder (with slanted sides) is still calculated using the same formula as a right cylinder:

V= πr2h

Provided that the height h is measured perpendicularly between the bases.

Read More: Area of Rectangle

Surface Area of a Cylinder

The surface area of a cylinder is just as important as volume. It determines how much material is required to cover the surface or paint the object.

Surface Area Formula:

A = 2πr2+ 2πrh = 2πr(r+ h)A

Where:

• 2πr2 is the area of the two circular bases

• 2πrh is the lateral (curved) surface area

This is particularly useful in manufacturing, where materials like labels or coatings are applied to cylindrical surfaces.

Volume of a Cylinder vs Volume of a Cone

A cylinder and a cone can have the same base and the same height, but the space each shape can hold is not the same. Although their outer shapes appear similar, their internal capacities are different. This is because of the way each shape is formed.

The volume of a cylinder is calculated using the below formula:

• Cylinder Volume = π × radius² × height

• Cone Volume = 1⁄3 × π × radius² × height

This means that, for the same radius and height, the cone always holds one-third the volume of the cylinder.

Let’s look at an example:

Suppose we have:

• Radius = 4 cm

• Height = 9 cm

Let’s calculate the volume for both the cylinder and the cone.

Cylinder Volume

V = π × 42 × 9 = π × 16 × 9 = 144π ≈ 452.39cm3

So the cylinder holds about 452.39 cubic centimeters.

Cone Volume

V = ⅓ × π × 42 × 9 = 13 × π × 16 × 9 = 48π ≈150.80 cm3

So the cone holds about 150.80 cubic centimeters.

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Real-Life Use of Volume of a Cylinder

The volume of a cylinder helps to find out how much space is inside a cylinder-shaped object. This is useful in many everyday situations:

• To know how much water a tank can hold

• To measure liquid in bottles, cans, or jars

• To find out how much concrete is needed for a pillar

• To calculate gas in a cylinder, like an oxygen tank

• To check how much liquid flows through a pipe

Read More:  How to Find the Area of a Polygon

Volume of a Cylinder Solved Examples

1. A cylindrical water tank has a radius of 70 cm and a height of 120 cm. How much water can it hold in litres? Use π = 3.14.

Solution: Volume = π × r2 × h = 3.14 × 702 × 120 = 3.14 × 4900 × 120 = 1,843,200 cm3

Convert to litres:

1,843,200 ÷ 1000 =1843.2 litres

The tank holds 1843.2 litres of water.

2. A hollow pipe is 1 meter long with an outer radius of 7 cm and an inner radius of 5 cm. What is its volume in cubic centimeters? Use π = 3.14.

Solution:  Convert height to cm: 1 m = 100 cm

Volume = π × h × (R2−r2) = 3.14 × 100 × (49 − 25) = 3.14 × 100 × 24 =7536 cm³

The pipe holds 7536 cm³ of material.

3. A concrete pillar is shaped like a cylinder with a diameter of 60 cm and height 3 m. Find the volume of concrete used in cubic meters. Use π = 3.14.

Solution: 

Radius = 60 ÷ 2 = 30 cm = 0.3 m, height = 3 m

Volume = π × r2 × h = 3.14 × 0.32 × 3 = 3.14 × 0.09 × 3 = 0.8484 m3

The pillar uses 0.8484 cubic meters of concrete.

4. A juice can is shaped like an oblique cylinder with radius 5 cm and vertical height 12 cm. What is its volume in cm³? Use π = 3.14.

Note: Oblique cylinders use the same formula as right cylinders if height is measured vertically.

Solution: Volume = 3.14 × 52 × 12 = 3.14 × 25 × 12 = 942 cm³

Answer: The can holds 942 cm³ of juice.

Also read:  Area of a Sector 

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