Volume of a Sphere
Lesson Objective
In this lesson, we will learn about the volume of a sphere.
About This Lesson
In this lesson, we will:
 Learn about the formula for the volume of a sphere
 See an example on using the formula to calculate the sphere's volume
 See another example on using the formula to calculate the radius of a sphere
The study tips and math video below will explain more.
Study Tips
Tip #1
If we have a sphere with the radius r, the volume, V of the cylinder is:
where π is a number that is approximately equals to 3.14.
The math video below will give more explanation on this formula. Also, we will see some examples on how to use it.
Math Video
Lesson Video
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00:00:03.030
In this lesson, we will learn about the volume of a sphere.
00:00:07.100
Let's start, consider this sphere. Now, this sphere has the radius r.
00:00:14.230
The formula to find the volume of this sphere, V is 4 over 3 pi r cube.
00:00:21.010
Let's see some examples on how to use this formula. For these examples, we take pi as, 3.14
00:00:30.160
First example, find the volume of this sphere when its radius is 4cm.
00:00:36.180
Since the radius is given as 4 cm, we can substitute 'r' with 4.
00:00:43.090
Now, let's simplify 4 cube. To do so, 4 cube is the same as 4 multiply by 4 multiply by 4, which is equals to 64.
00:00:54.100
Let's write this down here.
00:00:57.080
Next, since pi is given as 3.14. We can substitute this pi with 3.14.
00:01:05.060
From here, we can find the volume by calculating these numbers.
00:01:10.070
3.14 multiply by 64 gives 200.96.
00:01:16.020
Now, this term is the same as 4 multiply by 200.96 over the 3.
00:01:23.030
We can multiply 4 with 200.96. This gives 803.84.
00:01:30.160
Next, 803.84 divide by 3 gives 267.95.
00:01:37.220
Note that, this number has no meaning unless we include the unit for it.
00:01:43.000
Since the radius is in centimeter, the volume will be in cubic centimeter.
00:01:48.160
Hence, the volume of this sphere is 267.95 cubic centimeter.
00:01:56.140
Next example, the volume of this sphere is 113.04 cubic ft. Find its radius, r.
00:02:05.110
Now, let's begin with the formula for the volume of a sphere, V = 4 over 3 pi r cube.
00:02:12.130
Here, we can see that since the volume and pi are given, we can find the radius, r, by solving this equation for r. Here’s how.
00:02:22.190
First, it is easier to work with this equation if we rewrite it as, V equals 4 pi r cube, over 3.
00:02:31.140
Next, note that we can remove the fraction in this equation, by multiplying both sides of the equation with 3.
00:02:39.050
This gives, 3V equals to 4 pi r cube. Now, since pi is given as 3.14, we can substitute this pi with 3.14.
00:02:52.000
Next, we multiply 4 with 3.14. This gives 12.56.
00:02:58.220
Next, we can substitute V with 114.04.
00:03:04.060
3 multiply with 113.04 gives, 339.12.
00:03:11.170
Alright, now we have 12.56 r cube, equals to 339.12.
00:03:19.170
Let's rewrite this equation so it will looks neater.
00:03:23.220
Now, notice that, to get closer to find r, we need to remove 12.56.
00:03:31.080
To do so, we divide both sides of the equation with 12.56.
00:03:36.230
By doing so, we have r cube equals to, 339.12 over 12.56.
00:03:45.080
Next, we divide 339.12 with 12.56. This gives 27.
00:03:53.100
Now, since r cube is equals to 27, we can find r, by calculating the cube root of 27.
00:04:01.180
Cube root of 27 gives 3.
00:04:05.060
Again, this number has no meaning unless we include the unit for it.
00:04:10.000
Since the volume is in cubic feet, the radius of the sphere will be in feet.
00:04:15.060
Hence, the radius of the sphere is 3 ft.
00:04:20.030
This is all for this lesson. Try out the practice question to further your understanding.
End of the transcript for volume of a sphere
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 sphere or pick your choice of question below.
 Question 1 on finding the volume of a sphere
 Question 2 on finding the radius of a sphere
SiteSearch and Q&A Library
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