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High School Geometry: Tutoring Solution14 chapters | 161 lessons

Instructor:
*Yuanxin (Amy) Yang Alcocer*

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

Read this how-to lesson to learn what steps you need to take to find the volume for a sphere with a radius of 4. Learn what the formula is and how to use it.

In this lesson, you'll learn how to find the volume of a sphere with a radius of 4 inches. A **sphere** is a 3-dimensional round object. The **volume** is how space is inside the sphere. Bubbles are spheres. Basketballs are spheres. Water balloons are spheres. When you want to find out how much space is inside such a sphere, you'll follow these steps to calculate the volume of the sphere.

The pi symbol can be approximated by the number 3.14. The r stands for the radius. This formula tells you that you need to take your radius and cube it. You then multiply it by pi, then multiply by 4 and divide by 3.

If the radius is 4 inches, then your formula becomes this.

What happened here is that you plugged in 4 into the r for radius.

Your final step is that of evaluating your formula. If you are using a calculator, then you can use your calculator's symbol for pi. If not, then you can approximate pi with the number 3.14.

Evaluating your formula, you get this.

Your answer then is 267.95 inches cubed. Remember, you are dealing with volume, so your answer will always have units that are cubed. Why is this? Because, your formula tells you to cube the radius. Since the radius is in inches, then you also cube your inches. Thus your answer is 267.95 inches cubed.

Now, if your radius was 4 feet instead of 4 inches, then your answer would be 267.95 feet cubed.

Remember, if you don't write out your measurement units while you are evaluating the formula, you'll need to remember to write the measurement unit in for your answer and cube it.

Let's look at a real world example now.

Sammy is building a round fish tank for his goldfish. He's had his goldfish for 10 years now and his goldfish is now almost a 1 foot long! That's a big fish. And a big fish needs a big tank. So Sammy wants to build a round fish tank that has a radius of 4 feet. This way, his goldfish has plenty of room to swim around. How much space will Sammy's goldfish have inside his new tank?

To solve this problem, you'll need to follow the steps you just read.

First, start with the formula.

Next, you plug in 4 feet for the radius, r.

Your final step is to evaluate this formula. You get 267.95 feet cubed for your answer after evaluating. This is how much space Sammy's goldfish will have.

The really cool part about all the steps you just learned is that you can use this formula for any size sphere. All you have to do is to replace the r with your radius measurement, whatever that may be.

For example, if your radius is 5 inches, then you would plug in 5 inches for the radius and then evaluate. You get this.

Your answer is 523.33 inches cubed. Remember, your answer for volume always needs to be cubed.

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Lesson
11 in chapter 12 of the course:

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High School Geometry: Tutoring Solution14 chapters | 161 lessons

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