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Geometry: High School15 chapters | 160 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how you can find the surface area and volume of spheres. Learn the formulas and measurements you need to solve problems and discover how to identify spheres in the real world.

**Spheres** are three-dimensional shapes with no corners. Every point on the surface is the same distance from the center. We see spheres every day, and we don't think much about how they are defined.

Take a ball, for example. A ball is a sphere, but do we think about how it is defined? No, because most likely we will end up playing with it, bouncing it up and down. But take a close look, and you will see that it has no corners and that no matter how you hold the ball, every one of those points will be the same distance to the very center of the ball.

This distance from any point on the sphere's surface to the center of the sphere is called the **radius**. Because a sphere is a uniform shape, meaning that no matter how you turn it, it will always look the same, the radius is the only measurement we need.

The formula to find a sphere's **surface area**, the area of just the surface of a three-dimensional object, requires the radius measurement.

Surface Area = 4 * pi * *r*2

The *r* stands for the radius, and the pi is approximated by 3.14.

Once we know the radius, we can plug this information into our formula and evaluate to find our surface area. Let's see how this works.

Let's say we have a basketball whose radius is 5 inches, and we want to find the surface area. What do we do?

Well, we first check to see if we know the radius. Yes, the problem tells us that the radius of our sphere, our basketball, is 5 inches. Oh good, we can now simply plug this number into our formula and find our answer. So we plug in 5 in for *r*.

Surface Area = 4 * 3.14 * 52

I've replaced pi with its approximation of 3.14 as well. Now I square the 5 to get 25 and then multiply that with the rest to get my answer.

Surface Area = 4 * 3.14 * 25

Surface Area = 314 inches squared

My answer is 314 inches squared. I recall that area is always squared so I have to make sure my answer has my measurement units squared. Everything checks out and I am done.

To find a sphere's **volume**, the amount of space inside a three-dimensional object, we need to know only the radius as well. And the process is similar to that of finding the surface area, just with a different formula.

Volume = (4/3) * pi * *r*3

Let's see how this formula works by finding the volume of our basketball that has the radius of 5 inches. We see that we already know the radius, so we can plug that into our formula right away.

Volume = (4/3) * 3.14 * 53

Again, I've replaced pi with its approximation of 3.14. I continue by cubing my 5 to get 125. I then multiply the 125 with 3.14 and 4 and then I divide by 3 to get my answer.

Volume = (4/3) * 3.14 * 125

Volume = 523.33 inches cubed

So my answer is 523.33 inches cubed. Notice that my answer ends with my measuring units cubed. This is because volume is always cubed.

So now let's recap what we've learned. We've learned that **spheres** are three-dimensional shapes that have no corners and whose surface is the same distance to the center from anywhere. A basketball, or any ball for that matter, is an example of a sphere. The only measurement that we need to worry about is the **radius**, the distance between a point on the surface to the center of the sphere.

To find a sphere's **surface area**, the area of just the surface of a three-dimensional object, we use this formula:

Surface Area = 4 * pi * *r*2, where pi is approximated by 3.14 and *r* is the radius.

To find a sphere's **volume**, the amount of space inside a three-dimensional object, we use this formula:

Volume = (4/3) * pi * *r*3

Once we have the radius, all we have to do is plug that information into our formula so that we can find our surface area and volume.

After completion of this lesson, you should be able to:

- Define sphere
- Solve for the radius of a sphere
- Identify the formula for measuring a sphere's surface area
- Recognize how to find the volume of a sphere

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Geometry: High School15 chapters | 160 lessons

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