Cylinder Volume Calculator

This cylinder volume calculator allows you to determine the volume of a cylinder. Whether you need to estimate the amount of water that fits in a can, tea in a mug and similar stuff, this gizmo would calculate it all. 

What is the volume of a cylinder

A cylinder is a 3-dimensional tube with a particular length, height and area of cross-section. To give you a visual example, consider a metal pipe for water. This pipe has hollow cylindrical dimensions.

On the other hand, the example for conventional cylindrical dimensions would be a cylindrical candy without hollow surface. 

The volume of the cylinder, on the other hand, is the space that matter (solid, liquid or gas) would occupy in a given cylindrical container. 

Cylinder volume formula

The volume of a cylinder formula is given by:

\( \mathbf{Cylinder Volume} = \large{\pi r^2h}\) 

'r' represents the radius of the cylinder.

while

'h' represents the cylinder height.

This is the conventional cylinder volume equation. It also happens to be the formula for right cylinder volume.

How to find/calculate the volume of a cylinder

Once you are acquainted with the concept of the volume and its formulas, you can easily calculate cylinder volume. However, to give you a head-start, we have provided two examples: namely, the calculation of the right cylinder and hollow cylinder.

Right Cylinder Calc: find v

Let's first discuss the right cylinder calculation.

The formula for this particular calculation is the orthodox formula we have mentioned above. Now let's go ahead and determine the volume of a right cylinder.

• Consider that you have a cylinder with a height 'h' of \(20\mathrm{cm}\).
• And has a radius of \(2\mathrm{cm}\).
• As the end base of a cylinder is circular, we need pie as well, which is universally \(3.141\)

With all these values in our possession, we can begin to calculate the volume of a cylinder. So, let's begin the show!

It's a 3-step calculation

1- Given that we have the formula:

\(V = \large{\pi r^2h}\) 

2- We input the respective values in the equation

\(V = 3.14 (2^2) 20\)

3- Multiplying Pie value with the value of sqaured radius and height, we get:

\(V = 251.33\)

Hollow Cylinder

The hollow cylinder is a 3-dimensional surface bounded by two right circular cylinders possessing same axis and two parallel annular bases perpendicular to the cylinders' common axis. 

Okay let's rather describe it more easily: It is a cylindrical body which is hollow inside. 

The formula for the calculation of the volume of a hollow cylinder looks something like this.

Hollow cylinder volume = \(\pi \times (R^2 - r^2) \times h\)

where,

R stands for the external radius.

r stands for the internal radius.

While 

h stands for cylinder height.

And now that we have it's the formula, why not calculate it with hypothetical values for its variables.

• Consider this, the external radius of a hollow cylinder to be \(5\mathrm{cm}\).
• Consider the internal radius to be \(4.9\mathrm{cm}\).
• Consider that the given height of the cylinder is \(20\mathrm{cm}\).

Knowing these values, let's make our calculation.

1- The formula is given:

Hollow cylinder volume = \(\pi \times (R^2 - r^2) \times h\)

2- We input the hypothetical values in the formula. As the value of pie is universally 3.14 while the height of the hollow cylinder is 20 cm and external and internal radius are 5 and 4.9 cm respectively, we get:

V (hollow) = \(3.14 \times (5-4.9) \times 20\)

3- Subtracting internal radius from the external and multiplying pie with the product of cylinder height and the difference of external and internal radius, we get:

V (hollow) = \(3.14 \times (0.1) \times 20\)

V (hollow) = \(6.28\) 

4- so the volume of our hollow cylinder is \(6.28 \mathrm{cm}\).