How to Calculate Volume of a Cylinder? Formula or Equation with Diameter, Unit Gallons, Liters

Let’s explore Volume of a Cylinder!

How to Calculate Volume of a Cylinder? Formula or Equation with Diameter, Unit Gallons, Liters

We have used the volume of a cylinder in many areas, calculations, etc. What does it mean? In this article, we will learn its basics, definition of a cylinder, calculation, formula or equation, unit in Gallons or liters, many examples.

Let’s explore!

What is Volume of a Cylinder? Definition,  Examples

Volume of a Cylinder Basics

Have you seen a gas cylinder in your kitchen? How does it look like? Why do we call it a gas cylinder?

This is simple! It looks like a cylinder that consists of LPG gas.

More object for the cylinder can be as follows,

  • Piston chamber
  • Can
  • Shaft, etc.
how calculate volume cylinder formula diameter equation unit gallons
How to calculate volume cylinder formula diameter equation unit gallons

Now, we got the idea about the cylinder, so what about the volume of a cylindrical object-like gas cylinder or piston chamber?

It is nothing but the amount of space or materials it acquires.

Volume of a Cylinder Example

Let’s take a small can which is a cylindrical object to understand the meaning of cylindrical volume. Now, take some water in a bucket which has 5000ml water. The bucket has marked with a volume indicator in ml.

If you keep the can within the bucket water, then the surface area of water will raise 5200ml.

As per Archimedes’ principle, the can has replaced the same volume of water and this is the volume of the can, or simply the volume of a cylinder (Can).

  • This is an indirect method but do you know that it can be easily calculated by a simple equation or a formula? We will learn it!
  • It is not mandatory that it is required to be liquid, the same thing is applicable for solid as well. However, the material should be distributed uniformly in the cylinder.

Volume of a Cylinder Definition

The volume of a cylinder can be defined as the three dimensions shape whose base is circular. It can also be defined as a geometrical shape with straight parallel sides and a circular base.

Look at this below image of a cylinder, here,

  • All sides are parallel
  • Base is circular
volume cylinder definition examples
Volume of cylinder definition examples

Volume of Cylinder Formula or Equation with Diameter 

What is Volume of a Cylinder Formula or Equation? (Solid)

We have got a basic concept about the volume of a cylinder. Now, if you want to measure the volume, then there is a formula or equation of cylinder volume.

  • This formula is used to measure the capacity of the cylinder.
  • The amount of space available or required for a cylinder.
  • The amount of material can get from a cylinder.
  • The surface area can be calculated.
  • Base area or top area can be calculated.

Formula or equation for the volume of a cylinder can be written as,

  • Volume of a cylindrical object, V = Area of the circular base × Height of cylinder
  • V = π x (Radius)2 x Height of cylinder [Area of the circular base = π x (Radius)2]
  • V = πr2h
how calculate volume cylinder formula equation
How to calculate volume cylinder formula equation

Where,

  • r = Radius of the base of the cylinder
  • h = Height of cylinder

Volume of Cylinder with Diameter (Solid)

Based on the radius, we have seen that volume, V = πr2h

Now, we know that r = D/2,

Hence,

  • V = πr2h
  • V = π x (D/2)2h
  • V = π x (D2/4) h
  • V = π D2h/4

This is the volume of cylinder with diameter.

Volume of A Hollow Cylinder Formula or Equation 

We have already derived the equation of the volume of a solid cylinder. Now, what about the volume of a hollow cylinder?

Is the same formula can be used to derive the volume?

No, we cannot!

Let’s see what is the volume of a hollow cylinder!

A hollow cylinder means it has basically two radius.

  • The radius for the outer circular base, say, R
  • Another radius for the inner circular base, say, r

Also, consider the height of the cylinder is h.

how calculate volume hollow cylinder formula diameter equation
How to calculate volume hollow cylinder formula diameter equation

Now, the volume of the hollow cylinder means the difference between the volume of the outer cylinder and the inner cylinder.

  • Volume of outer cylinder = Vo = πR2h
  • Volume of inner cylinder = Vi = πr2h

So, the difference of the volume, Vh

  • Vh = Vo – Vi
  • Vh = πR2h – πr2h
  • Vh = πh(R2– r2)

Volume of Hollow Cylinder with Diameter 

Based on the radius, we have seen that volume, Vh = πh(R2– r2)

Now, we know that r = D/2,

Hence, Vh can be written as,

  • Vh = πh(R2– r2)
  • Vh = πh[(D/2)2– (d/2)2]
  • Vh = πh[D2/4 –  d2/4]
  • Vh = πh(D2 –  d2)/4

Volume of Cylinder Units in Gallons & Liters

Volume of Cylinder Basic Units

The unit of volume of a cylinder can be, as follows

Volume of a Cylindrical object = πr2h

The unit of volume of a Cylindrical object = π x (unit of radius)2 x unit of height

In S.I unit

  • The S.I unit of volume of a Cylinder = π x (m)2 x m = m3 [π is unitless

In C.G.S unit

  • The C.G.S unit of volume of a Cylindrical object = π x (cm)2 x cm = cm3 or cc [π is unitless number]
  • 1 litre = 1000 cm3 = 1000 cc

In F.P.S unit

  • The F.P.S unit of volume of a Cylinder = π x (ft)2 x ft = ft3 [π is unitless number]
  • number]

Volume of Cylinder in Gallons & Liters

Let’s see the units of volume of the cylinder in U.S gallons (widely used).

  • ​1 liter​ = 0.264 U.S. gallons [Remember this value]
  • or, 1000 cm³ = 0.264 U.S. gallons [ as 1 liter = 1000 cm³]
  • ​1000 000 cm³ = 264 U.S. gallons [ Multiplying 1000 in both side]
  • 1 m³ = 264 U.S. gallons [ as 1 m³ =1000 000 cm³]
  • 3.28 x 3.28 x 3.28 ft³ = 264 U.S. gallons [ as 1 m = 3.28 ft]
  • 1 ft³ = 264/(3.28 x 3.28 x 3.28) = 7.48 U.S. gallons
  • ​1 milliliter​ = 1/1000 liter = 264/1000 U.S. gallons = 0.264 U.S. gallons

There are so many worksheets for volume of cylinder available on the internet for practice.

How to Derive Volume of a Cylinder?

As per the formula of volume of cylinder, we have seen if we get radius and height, then we can easily find out the volume of a cylinder. So, the volume of a cylinder can be derived based on the following a few simple steps,

  • Radius of the circular base
  • Area of circular base
  • Height of the cylinder
  • Find out the volume of a cylinder

Radius of circular base

Firstly, we must get the radius of the circle of the base of cylinder.

  • If the data is available, then you can use it as radius, ‘r’
  • If the diameter, ‘D’ is given, then radius = diameter/2, or r = D/2.
  • If perimeter, p is given, we can get ‘r’ from it. We know, p=2πr, or r = p/2π .
radius circular base cylinder example
Radius of circular base cylinder example

Let’s check a few examples,

  • a circle has a diameter, D = 30cm. So, it’s radius, r = D/2 = 30/2 = 15 cm.
  • a circle has a perimeter p =40π cm. So, it’s radius, r = p/2π = 40 π/2π = 20 cm.

Area of circular base

Secondly, we have to calculate the area of the circular base from the radius of the base circle. It is very easy, as there is an equation of circular base area.

Area of a circle, A = πr2

area circular base cylinder
Area of circular base cylinder

Now, we have calculated the radius 15 cm and 20 cm in the first steps.

  • The area of circular base of having 15 cm radius = πr2 = π x 152 = 225π = 706.5 cm2 [π = 3.14]
  • The area of circular base of having 20 cm radius = πr2 = π x 202 = 400π = 1256 cm2 [π = 3.14]

Height of the cylinder

As height, ‘h’ is in the formula of volume of a cylinder, we have to get this value as well.

height of cylinder
Height of cylinder
  • If the value of height is given, straightway it can be used.
  • It can be measured from the drawing.
  • Say, the cylinder has a height about 50cm.

Find out the volume of a cylinder

Here comes the final step to calculate the volume of a cylindrical object. It can be done as follows,

Method-1

Simply, the value of ‘r’ and ‘h’ can be put in the volume of cylindrical object formula πr2h

Volume of cylinder, V

  • V = πr2h
  • V = 3.14 x 152 x 50 [where, r = 15cm and h = 50cm]
  • V = 35325 cm3

Method-2

Another method, multiplying the value of area and height of the cylinder.

Volume of cylinder, V

  • V Area x Height
  • V = πr2 x h
  • V = 706.5 x 50 [where, πr2 = 706.5cm and h = 50cm]
  • V = 35325 cm3

Applications of Cylinder’s Volume Formula

There are thousands of examples of cylindrical objects in our daily life. If you know the formula of cylindrical volume, you can calculate the volume.

Manufacturers are used to design these all objects considering the formula.

Let’s see a few examples of cylindrical volumes,

  • Cylindrical Battery
  • Cylindrical flasks
  • Test tubes
  • Cylindrical tanks for chemicals, water, etc.
  • Cylindrical bottles
  • Cylindrical cups
  • Cylindrical glasses

Volume of Cylinder Calculation Problems 

Let’s see a couple of problems for the volume of cylindrical object’s calculations to clear the total concept.

Question 1

Find out the volume of a cylindrical water tank with a circular base of a radius of 25 cm and a height of 30 cm.

Solution

Input data

  • Circular base radius of the cylindrical water tank, r = 25 cm
  • Cylindrical water tank height, h = 30 cm

As per the formula of volume of a cylindrical tank, V = πr2h

Hence, volume, V

  • V = πr2h
  • V = 22/7 × 252× 30
  • V = 58929 cm3

As it comes in cm3, and it is a big number, we can short it out in liters.

We already learned that 1 liter = 1000 cm3

Or, we can say, 1000 cm3 = 1 liter

∴ 58929 cm3 = 58929 / 103 = 58.93 litres

The volume of the cylindrical water tank is 58.93 liters.

Question 2

Find out the radius of a cylindrical water tank with a volume of 220 m³ and a height of 10 m. (Take π = 22/7)

Solution

Input data

  • The volume of the cylindrical tank, V = 220 m³
  • Height of the cylindrical tank = 10 m

As per the formula of volume of a cylindrical tank, V = πr2h

Hence, volume,

V = πr2h

220 = πr2h

=> πr2h = 220

=> r2= 220/ πh = 220 / (22/7 × 10)

=> r² = 220 x 7 / (22 x 10)

=> r² = 220 x 7 / (22 x10)

=> r = 7 m

∴  r = 7 m

Hence, the radius of a cylindrical water tank is 7 m.

Question 3

Find out the height of a cylindrical steel object with a volume of 2464 m³ and a radius of 4 m. (Take π = 22/7)

Solution

Input data

  • The volume of the cylindrical object, V = 2464 m³
  • Radius of the cylindrical object, r = 4 m

As per the formula of volume of a cylindrical object, V = πr2h

Hence, volume,

V = πr2h

2464 = πr2h

=> πr2h = 2464

=> h = 2464/ πr2 = 2464 / (22/7 × 42)

=> h = 2464 x 7 / (22 x 16)

=> h = 7 x 7

=> h = 49 m

∴  h = 49 m

Hence, the height of a cylindrical object is 49 m.

Question 4

A cylindrical hollow pipe has water. The outer diameter of the hollow pipe is 8 cm and the inner diameter is 6 cm. The length of the pipe is 14 cm.

Find out the volume of water in the hollow pipe.

Solution

Input data

  • The diameter for the outer circular base, D = 8 cm
  • The radius for the outer circular base, R = D/2 = 8/2 = 4 cm
  • The diameter for the inner circular base, d = 6 cm
  • The radius for the inner circular base, r = 6/2 = 3 cm

The length of the cylinder = height of the cylinder = 14 cm.

So, h = 14 cm

Now, from the formula of cylinder,

  • Volume of outer cylinder = Vo = πR2h
  • Volume of inner cylinder = Vi = πr2h

So, the volume of hollow pipe =  the difference of the volume, Vh

  • Vh = Vo – Vi
  • Vh = πR2h – πr2h
  • Vh = πh(R2– r2)
  • Vh = (22/7) x 14 x (42– 32)
  • Vh = (22/7) x 14 x 7
  • Vh = 22 x 14
  • Vh = 308 cm3

The Volume of water in the pipe is 308 cm3

Conclusion

Hence, we have got the basics of the volume of a cylindrical shape, how to calculate, along with many calculations. Any queries, please feel free to contact us.

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