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Volume of Cylinder: Definition, Formula & Examples

finding volume of cylinders

Do you face challenges while finding the volume of a cylinder if its shape is distorted? Have you thought about how you find the volume of such cylinders? That’s what you’ll be learning in about a moment. 

The volume of a cylinder means the space inside the cylinder that can hold a specific amount of material quantity. In simpler words, the capacity of a cylinder to hold a thing is its volume. Inside the space of a cylinder, you can hold either of the three types of matter – solid, liquid, or gas. This capacity can only be witnessed in a three-dimensional cylinder, i.e., you cannot hold any liquid, solid, or gas in a two-dimensional cylinder. 

A perfect three-dimensional cylinder has two congruent and parallel identical bases. This is known as the right circular cylinder. In a right circular cylinder, the bases are circular, and each line segment is a part of the lateral curved surface, which is perpendicular to the bases. You might have seen the right circular cylinders in your daily life. The shapes of cans, the shapes of paper rolls, straight glass, and many other places. 

However, if the shape of the glass is perfectly straight, it will be called a right circular cylinder. If the shape is not linear, then what will the shape be? 

If the two congruent and identical parallel sides somehow become non-parallel or are distorted, you will get either of the following cylinders:

  1. Oblique cylinder – It is a cylinder whose sides lean over the base at an angle that is not equal to a right angle. This will be the shape of the distorted glass that was discussed above. 
  2. Elliptic cylinder – It is a cylinder whose bases are ellipses. 
  3. Right circular hollow cylinder – It has the shape of a right circular cylinder. However, there are no closed circles at the end. 

How to Find The Volume of a Cylinder – Traditional Method 

It’s easier than you thought to find the volume of a cylinder. If you are still wondering how do you find the volume of a cylinder, all you need is a tub of water, a weighing scale, and an empty flat surface on which the tub can be placed. 

Place the tub on the flat empty surface and start filling it with water. You have to make sure that the water is filled up to the brim. Once the tub is filled with water, place your cylinder, whose volume you need to find, inside the tub. You will observe the water start to come out of the tub. 

Collect the fallen water in a beaker. Ensure that the water does not fall while you do the conversion. Place the beaker on a weighing scale and record the weight of the water. Remember to subtract the weight of the beaker. You must have only the weight of the water. 

According to the Archimedes Principle, the weight of the water falling from the tub will be equal to the weight of the cylinder. Hence, the weight of the water you get will be equal to the weight of the cylinder. You might be wondering then how do I find the volume of a cylinder? 

As per Physics, if you are in a room temperature place, the weight will be equal to the volume. That means 1 kg will be equivalent to 1 liter and so on. Hence, you will get the volume of the cylinder from the volume of the water. 

But, what if your place is in a cold or hot region? Then you have to use the other method. 

Formula to Find Volume of a Cylinder

You can find the volume of a cylinder by using the formula. This is universal and can be applied irrespective of your region. The volume units are cubic centimeters, cubic inches, or any standard unit with the word ‘cubic’ prefixed. 

There are two methods to find the volume of a cylinder. They are:

  1. Using the area and height
  2. Using the dimensions
  • Finding the volume of cylinders using area and height is nothing but a product of the area and height of any shape. This rule is valid for all the 3D shapes known in mathematics. For example, in a cuboid, if you know the area of one side of it and then multiply it by the height or width, i.e., the remaining side, you will get the volume.

In cylinders, V = area x height 

  • Finding the area with the known dimensions – The universal formula to find the volume of a cylinder is π r2 h, where the value of π (pi) is 3.14 or 22/7, r is the radius of the top or bottom of the cylinder, and h is the height. Using the formula, you can find the volume of the right circular cylinders and oblique cylinders. 

However, for elliptical cylinders, the formula is not the same. Since elliptical cylinders have varying radii, the formula to find their volumes is given by: V = π abh, where π = 22/7 or 3.14, a and b are the radii of the base of the elliptical cylinder, and h is the height.

Moreover, the formula is also different for the hollow right circular cylinders. The volume of a hollow right circular cylinder is given by: V = π (R2 – r2) h, where R is the outer radius of the circular base, r is the inner radius, and h is the height of the cylinder. 

If you are looking for the surface area formula of a cylinder, here it is A = 2πr+ 2πrh, where r and h are the radius and height of the cylinder, respectively. The units of surface area will be square units. 

Steps to calculate the volume of a cylinder

By following the given methods below, you can find the volume of a cylinder.

Step 1: Identify the type of cylinder given to you in the question or in real life. 

Step 2: Once you have the type of cylinder, you need to figure out the formula that can be used to find the volume of the cylinder. 

Step 3: Now you have the formula too. Check which dimensions you need to find the volume. Make sure all the dimensions have the same units. 

Step 4: Put them in their respective places and calculate the volume.

Step 5: Keep the units after the calculated value as ‘cubic units’. Use the respective unit, such as meter, centimeter, or any other, in place of the word unit. 

Examples to Find The Volume of a Cylinder

Example 1: A cylinder has a radius of 50 cm and a height of 100 cm. How to find the volume of a cylinder? 

Solution: We know the volume of a cylinder is given by the formula – π r2 h, where r is the radius of the cylinder and h is the height.

Therefore, putting the values, we get, 

V = π r2 h

= 3.14 x 502 x 100 = 785,000 cm3

Example 2: How do you find the volume of a cylinder whose one of the radii is 40 cm and another is 60 cm? The cylinder has a height of 200 cm. 

Solution: From the data given, you can find that the cylinder is elliptical as the radii are different. To find the volume of an elliptical cylinder, the formula is V = π abh, where a, and b are radii, and h is the height. 

Therefore, the volume of a cylinder = V = π abh

= π x 40 x 60 x 200 = 1507200 cm3

Example 3: How do you find the volume of a hollow cylinder from the inside and has outer and inner radii of units 6 and 8, respectively? The height of this hollow cylinder is 15 units. 

Solution: We know the formula for the volume of a hollow cylinder is given by V = π (R2 – r2) h.

Therefore, putting the values, we get, 

V = π (R2 – r2) h

= π (82 – 62) 15 = 1318.8 units2

Example 4: One day, Alex was wondering, “How do I find the volume of a cylinder whose height is 6 inches and radius is 3 inches.” Can you help her to find the volume of that cylinder?

Answer: Yes, you can! You know the formula to find the volume of a cylinder is given by: V = π r2 h.

Therefore, by putting the values, you get, V = π r2

= π x 32 x 6 = 169.56 in3

You can tell Alex that the volume of the cylinder is 169.56 in3

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