### Volume of a Cylinder

#### Lesson Objective

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

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 another 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 explanation about this formula. Also, we will see some examples on how to use it.

### Math Video

#### Lesson Video

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#### Math Video Transcript

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

00:00:07.090
Letâ€™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.

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