### Volume of a Sphere #### Lesson Objective

In this lesson, we will learn about the volume of a sphere. 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 You can contribute to the development of this site and keep it free by getting all six video lessons and volume of solids and calculator app for just US\$1.99 from Apple App Store.

I'd like to contribute or to know more about the app #### Math Video Transcript

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

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Let's start, consider this sphere. Now, this sphere has the radius r.

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The formula to find the volume of this sphere, V is 4 over 3 pi r cube.

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Let's see some examples on how to use this formula. For these examples, we take pi as, 3.14

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First example, find the volume of this sphere when its radius is 4cm.

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Since the radius is given as 4 cm, we can substitute 'r' with 4.

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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.

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Let's write this down here.

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Next, since pi is given as 3.14. We can substitute this pi with 3.14.

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From here, we can find the volume by calculating these numbers.

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3.14 multiply by 64 gives 200.96.

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Now, this term is the same as 4 multiply by 200.96 over the 3.

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We can multiply 4 with 200.96. This gives 803.84.

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Next, 803.84 divide by 3 gives 267.95.

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Note that, this number has no meaning unless we include the unit for it.

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Since the radius is in centimeter, the volume will be in cubic centimeter.

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Hence, the volume of this sphere is 267.95 cubic centimeter.

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Next example, the volume of this sphere is 113.04 cubic ft. Find its radius, r.

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Now, let's begin with the formula for the volume of a sphere, V = 4 over 3 pi r cube.

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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.

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First, it is easier to work with this equation if we rewrite it as, V equals 4 pi r cube, over 3.

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Next, note that we can remove the fraction in this equation, by multiplying both sides of the equation with 3.

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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.

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Next, we multiply 4 with 3.14. This gives 12.56.

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Next, we can substitute V with 114.04.

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3 multiply with 113.04 gives, 339.12.

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Alright, now we have 12.56 r cube, equals to 339.12.

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Let's rewrite this equation so it will looks neater.

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Now, notice that, to get closer to find r, we need to remove 12.56.

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To do so, we divide both sides of the equation with 12.56.

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By doing so, we have r cube equals to, 339.12 over 12.56.

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Next, we divide 339.12 with 12.56. This gives 27.

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Now, since r cube is equals to 27, we can find r, by calculating the cube root of 27.

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Cube root of 27 gives 3.

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Again, this number has no meaning unless we include the unit for it.

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Since the volume is in cubic feet, the radius of the sphere will be in feet.

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Hence, the radius of the sphere is 3 ft.

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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.

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