What is the formula of CSA of hollow cylinder?

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r1 = outer radius

π = pi = 3.1415926535898

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This calculator will calculate the various properties of a tube, also called a pipe or hollow cylinder, given 3 known values from variables of radii, circumference, wall thickness and height. A geometric solid tube is generally a cylinder with an end profile represented by an annulus.

Units: Note that units are shown for convenience but do not affect the calculations.  The units are in place to give an indication of the order of the results such as ft, ft2 or ft3.  For example, if you are starting with mm and you know r and h in mm, your calculations will result with C in mm, V in mm3, L in mm2, and A in mm2.

Below are the standard formulas for a tube.  Calculations are based on algebraic manipulation of these standard formulas.

Tube Formulas in terms of radius and height, r and h:

• Circumference, C:
  • generally C = 2πr, therefore,
  • C1 = 2πr1
  • C2 = 2πr2
• Lateral Surface Area, L, for a cylinder:
  • generally L = C * h = 2πrh, therefore,
  • L1 = 2πr1h, the external surface area
  • L2 = 2πr2h, the internal surface area
• Area, A, for the end cross section of the tube:
  • generally A = πr2, for a circle, therefore,
  • A1 = πr12 for the area enclosed by C1
  • A2 = πr22 for the area enclosed by C2
  • A = A1 - A2 for the area of the solid cross section of the tube, the end.
  • A = π(r12 - r22)
• Volume, V, for a cylinder:
  • generally V = A * h = πr2h, therefore,
  • V1 = πr12h for the volume enclosed by C1
  • V2 = πr22h for the volume enclosed by C2
  • V = V1 - V2 for the volume of the solid, the tube.
  • V = π(r12 - r22)h
• Thickness of the tube wall, t:

References

CalculatorSoup: Cylinder Calculator and Annulus Calculator

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.

Volume of a Hollow Cylinder Formula

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

Derivation of the Volume of a 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

How to Find Volume of 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.

1. Example 1: Find the volume of a hollow cylinder having inner radius = 6 cm, outer radius = 8 cm and height = 7 cm. (Use π = 22/7)

   Solution:

   Given: Inner radius of the hollow cylinder (r) = 6 cm Outer radius of the hollow cylinder (R) = 8 cm

   Height of the hollow cylinder (h) = 7 cm

Volume of the given hollow cylinder = π (R2- r2) h = (22/7)(82 - 62)(7) = 22(64 - 36) = 616 cm3

Answer: Volume of the given hollow cylinder = 616 cm3

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FAQs on 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.