Volume of a Cylinder

Lesson Objective

In this lesson, we will learn about the volume of a cylinder.

About This Lesson

In this lesson, we will:

Learn how to derive the formula for the volume of a cylinder
See an example on using the formula to calculate the cylinder's volume
See an example on using the formula to calculate the height of a cylinder

The study tips and math video below will explain more.

Study Tips

Tip #1

If we have a cylinder with the radius r and height h, the volume, V of the cylinder is:

V = πr²h

where π is a number that is approximately equals to 3.14.

The math video below will give more explanations about this formula. Also, we will see some examples on how to use it.

Math Video

Lesson Video

If the above player doesn't work, try this direct link.

Math Video Transcript

00:00:03.060
In this lesson, we will learn about the volume of a cylinder.

00:00:07.090
Let’s start, consider this circle with the radius r.

00:00:12.040
By now, we should already know that the area, A, of this circle is pi r square.

00:00:18.080
Next, let's change this circle into a cylinder.

00:00:22.140
After doing so, this cylinder has the radius r, and the height h.

00:00:29.000
Now, to find the volume of this cylinder, V, we just multiply the area, A with the height, h.

00:00:38.100
Hence, we multiply pi r square, with h.

00:00:43.070
This gives the formula for the volume of a cylinder, V equal pi r square h.

00:00:51.080
Now, it is important that we include the unit for volume.

00:00:55.170
Since the unit is not given, we can write the unit as cubic unit.

00:01:01.210
Alright, let's see some examples on finding the volume of a cylinder. For these examples, we take pi as 3.14.

00:01:11.200
Find the volume of this cylinder which has the radius 3cm and the height 5cm.

00:01:18.140
Let's start by using the formula, V equal pi r square h.

00:01:24.040
Now, since the radius is given as 3 cm, we can substitute 'r' with 3.

00:01:31.140
Next, let's simplify 3 square. Here, we can see that 3 square equals to 3 multiply by 3. This gives 9. Let's write this down here.  

00:01:46.180
Let's continue. The height h is given as 5 cm. Hence, we can substitute h with 5.

00:01:54.240
Now, we can simplify this equation by multiplying 9 with 5. This gives 45.

00:02:02.220
Next, pi is given as 3.14. So, let's substitute pi with 3.14.

00:02:12.140
Finally, we can find the volume by multiplying 3.14 with 45. This gives 141.30.

00:02:23.110
Note that, this number has no meaning unless we include the unit for it.

00:02:28.190
Since the radius and height are in centimeter, the volume will be in cubic centimeter.

00:02:34.200
Hence, the volume of this cylinder is 141.30 cubic centimeter.

00:02:42.130
Next example, the volume of this cylinder is 50 cubic ft and its radius is 2ft. Find its height, h.

00:02:51.180
Now, let's begin with the formula, V = pi r square h.

00:02:57.130
Since the volume of the cylinder is given as 50, we can substitute V with 50.

00:03:03.230
Next, since the radius is given as 2, we can substitute r with 2.

00:03:10.050
Now, let's simplify 2 square. 2 square is actually, 2 multiply by 2 which is equals to 4. Let's write this down here.  

00:03:22.120
Next, we can substitute pi with 3.14.

00:03:27.120
Here, we can simplify this equation by multiplying 3.14 with 4.

00:03:33.120
This gives 12.56.

00:03:36.240
Now, we have 12.56 h equals to 50. Let's rewrite this equation so it will be easier to see.

00:03:46.230
Next, to solve for 'H', we divide both sides of the equation with 12.56.

00:03:54.140
This gives, h equals to, 50 divided by 12.56.

00:04:01.180
Now, we can find h by dividing 50 with 12.56. This gives 3.98.

00:04:10.180
Again, this number has no meaning unless we include the unit for it.

00:04:15.180
Since the radius is in feet, the height of the cylinder will also be in feet.

00:04:21.060
Hence, the height of the cylinder is 3.98 ft.

00:04:27.090
That is all for this lesson. Try out the practice question to test your understanding.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on the volume of a cylinder or pick your choice of question below.

Question 1 on finding the volume of a cylinder
Question 2 on finding the height of a cylinder

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