Volume of a Cone
In this lesson, we will learn about the volume of a cone.
About This Lesson
In this lesson, we will:
Learn about the formula for the volume of a cone and see how it is related to the volume of a cylinder.
Look at an example on using the formula to calculate the cone's volume
Look at another example on using the formula to calculate the base radius of a cone
below will explain more.
In the previous lesson, we learn that the volume of a cylinder is
. Now, the volume of a cone is one third of the cylinder's volume.
Hence, for a cone with height
and base radius
, the volume,
of the cone will be:
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.
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Math Video Transcript
00:00:03.140 In this lesson, we will learn about the volume of a cone. 00:00:07.230 Consider a cylinder with the height h, and base radius r. 00:00:13.120 Now, we already know that the volume of a cylinder, V, is pi r square h. 00:00:20.120 With this, let's change this cylinder into a cone. 00:00:26.040 Now, we have a cone with the height h, and base radius r. 00:00:31.120 Base on calculations, the volume of the cone found to be one third of a volume of a cylinder. 00:00:38.000 Therefore, the volume of a cone, V, is one third pi r square h. 00:00:45.090 Let's see some examples on using this formula. For these examples, we take pi as 3.14. 00:00:55.090 Find the volume of this cone when its height is 5cm, and its base radius is 3cm. 00:01:02.040 Now, we start with the formula for the volume of a cone, V equal 1 third pi r square h. 00:01:09.180 Since the radius is 3cm, we can substitute r with 3. 00:01:15.220 Now, let's simplify 3 square. 3 square is the same as 3 multiply by 3. This gives 9. 00:01:26.080 Let's put this back here. 00:01:29.140 Next, since the height is given as 5 cm, we can substitute h with 5. 00:01:36.220 We can simplify by multiplying 9 with 5. This gives 45. 00:01:43.160 Next, since pi is given as 3.14, we can substitute this pi with 3.14. 00:01:52.020 3.14 multiply by 45 gives 141.30. 00:01:59.020 Now, this term is the same as, 1 bracket 141.30, over 3. 00:02:07.020 1 multiply by 141.30 gives back 141.30. 00:02:14.120 141.30 divides by 3, gives 47.10. 00:02:21.150 Now, this number has no meaning unless we include the units for it. 00:02:26.130 Since the units are given in centimeter, the volume will be in cubic centimeter. 00:02:32.160 There, the volume of this cone is 47.10 cubic centimeter. 00:02:40.120 Next example, the volume of this cone is 12.56 cubic feet, and its height is 3cm. Find its radius, r. 00:02:51.180 To solve this, we start with the formula for the volume of a cone, V equals 1 third pi r square h. 00:03:00.010 Here, we can see that since the volume, pi, and h are given, we can find r, by solving this equation for r. Here’s how. 00:03:11.140 First, it is easier to work with this equation if we write 1 third pi r square h in the form of fraction. By doing so, we have, 1 pi r square h, over 3. 00:03:25.040 1 pi r square h is the same as, pi r square h. 00:03:31:040 Next, note that we can remove the fraction in this equation, by multiplying both sides of the equation with 3. 00:03:39.160 This gives, 3 'V' equals to pi r square h. 00:03:45.130 Now, the volume of the cone is 12.56 ft. Hence, we can substitute V with 12.56. 00:03:53.220 3 multiply by 12.56 gives 37.68 00:04:00.020 Next, since the height of the cone is 3 ft, we can substitute h with 3. 00:04:07.020 Similarly, since pi is given as 3.14, we can substitute this pi with 3.14. 00:04:15.180 We can simplify by multiplying 3.14 with 3. This gives 9.42. 00:04:24.040 Alright, now we have 9.42 r square, equals to, 37.68. 00:04:32.130 Let's rewrite this, so it will look neater. 00:04:36.230 To get closer to finding r, we need to remove 9.42. 00:04:43.090 We can do so, by dividing both sides of the equation with 9.42. This gives, r square equals to 37.68 over 9.42. 00:04:57.080 37.68 divides by 9.42, gives 4. 00:05:04.010 Now, since r square is equals to 4, we can find r, by calculating the square root of 4. 00:05:13.040 Square root of 4 gives 2. 00:05:16.240 Again, this number has no meaning unless we include the unit for it. 00:05:22.050 Since the volume is in cubic feet, the radius of the base of this cone will be in feet. 00:05:28.170 Hence, the radius of the base of this cone is 2 ft. 00:05:35.180 This is all for this lesson. Try out the practice question to further 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 cone
or pick your choice of question below.
on finding the volume of a cone
on finding the base radius of a cone
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