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.
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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