Volume of Hollow Cylinder

The volume of a hollow cylinder is defined as the three-dimensional space enclosed by it. For example, the volume of glass tells us about the available space inside it. In other words, volume tells the maximum space that can be occupied by water if the water is poured into the glass.

A hollow cylinder is a cylinder that is empty from the inside and has some difference between the internal and external radius. In other words, it is a cylinder that is empty from the inside and has some thickness at the peripheral. The shape formed at the bottom of a hollow cylinder is called an annular ring, i.e. it is a region bounded by two concentric circles. In this section, we will discuss the volume of a hollow cylinder along with solved examples.

The cylinder is a three-dimensional shape that has a circular base. A cylinder can be observed as a set of circular disks that are stacked on one another. While a hollow cylinder is defined as a cylinder that is empty from the inside and has some difference between the internal and external radius.

For a given hollow cylinder, with both outer radius and inner radius known, its volume can be given by:

Volume of a hollow cylinder, V = π (R² - r²) h cubic units
Where,

• R = outer radius
• r = inner radius
• h = height of the hollow cylinder

The formula to calculate the volume of a cylinder is given as,

Volume of a cylinder = Base area × Height = (π R²) × h cubic units
Where,

• R = Radius of a cylinder
• h = Height of cylinder

The volume of a hollow cylinder having outer radius, 'R' and inner radius, 'r' can be written as the volume of a solid cylinder of radius, 'R' and height, 'h' minus the volume of a solid cylinder of radius, 'r' and height, 'h',

Therefore, Volume of a hollow cylinder = External cylinder volume - Internal cylinder volume
⇒ Volume of hollow cylinder = π R² h - π r² h = π (R² - r²) h cubic units

where,

• R = outer radius,
• r = inner radius, and,
• h = height of the hollow cylinder

To calculate the volume of a hollow cylinder with a given outer radius, 'R', inner radius, 'r', and height, 'h', we can follow the steps given below,

• Step 1: Note down the known dimensions of the hollow cylinder and check that they should have the same units.
• Step 2: Apply the formula to calculate the volume of a hollow cylinder, Volume of hollow cylinder = π (R² - r²) h
• Step 3: Represent the answer with units.

Example: How to find the volume of a hollow cylinder having inner radius = 20 units, outer radius = 30 units, and height = 21 units? (Use π = 22/7)

Solution: Volume of the given hollow cylinder = π (R² - r²) h = (22/7)(30² - 20²)(21) = 66(30 - 20)(30 + 20) = 33,000 cubic units.

Now, that we have understood the formula and method to find the volume of a hollow cylinder, let us have a look at a few solved examples in the next section.

What Is the Volume of a Hollow Cylinder?

The volume of a hollow cylinder is defined as the space enclosed by the shape in a three-dimensional plane. A hollow cylinder is one that is empty from the inside and has some difference between the internal and external radius. In other words, it is a cylinder that is empty from the inside and has some thickness at the peripheral.

What Is the Formula to Calculate the Volume of a Hollow Cylinder?

The formula to calculate the volume of a hollow cylinder is given as, Volume of hollow cylinder = π (R² - r²) h cubic units, where, 'R' is the outer radius, 'r' is the inner radius, and, 'h' is the height of the hollow cylinder.

How to Find Volume of Hollow Cylinder in Liters?

To find the volume of the hollow cylinder in liters, we can convert the value in liters using the below conversion, i.e.,
1 Litre = 1000 cubic cm or cm³
For example: A cylindrical tube having a volume of 1000 cm³ is equivalent to having a capacity of 1L.

What Is the Unit Used to Express Volume of Hollow Cylinder?

In measurement, the volume of the hollow cylinder is expressed in cubic units, like m³, cm³, ft³, in³, yd³, etc. Other common units used are liters(l) and millimeters(ml).

How Does the Volume of a Hollow Cylinder Change When the Height is Doubled?

The volume of a hollow cylinder is directly proportional to the height of the hollow cylinder. Therefore, the volume gets doubled when the height of the hollow cylinder is doubled.

How Do You Find the Volume of a Hollow Cylinder if Only Base Area and Height Is Given?

The volume of a cylinder is the total capacity of the cylinder, thus signifying the amount of any material that can be immersed in it or the amount of any material it can hold. From the definition, the volume of the cylinder = Base Area × Height

What Is the Annular Ring of a Hollow Cylinder?

The 2D shape formed at the bottom of a hollow cylinder is called an annular ring, i.e. it is a region bounded by two concentric circles. The base area of the hollow cylinder is the area of the annular ring of the cylinder.