### 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

#### Site-Search and Q&A Library

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