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Finding the Volume for a Sphere with a Radius of 4: How-To & Steps

Instructor
Yuanxin (Amy) Yang Alcocer

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

Expert Contributor
Robert Ferdinand

Robert Ferdinand has taught university-level mathematics, statistics and computer science from freshmen to senior level. Robert has a PhD in Applied Mathematics.

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.

The Steps

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.

Step 1: Use the formula for the volume of a sphere.

volume of a 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.

Step 2: Plug in 4 for the radius.

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

volume of a sphere

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

Step 3: Evaluate the formula.

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.

volume of a sphere

The Solution

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.

Real World Example

Let's look at a real world example now.

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Additional Activities

Practice Questions to Find the Volume of a Sphere (Please Show All Your Work - You Will Need a Calculator with pi)

1. Find the volume of a sphere whose diameter is 24 meters (m).

2. Find the volume of the spherical planet XLV. The radius of XLV is 32000 kilometers (km).

3. Two hemispherical pieces of plaster, each having diameter 2 cm, are joined together along their flat surfaces. What is the volume of the resulting sphere?

Answers (To Check Your Work)

1. Since the diameter of the hemisphere is 24 m, its radius r = 24/2 = 12 m.

Hence, using the volume formula, the volume of this hemisphere will be:

V = (4/3) x pi x r^3 = (4/3) x pi x (12^3) = 7238.22 m^3 (to two decimal places).

2. The radius of the spherical planet XLV is given as r = 32000 km. Therefore, the volume of XLV will be the volume of a sphere which is:

V = (4/3) x pi x r^3 = (4/3) x pi x (32000^3) = 1.37 x 10^(14) km^3.

3. When the two hemispherical pieces of plaster are joined together along their flat surfaces, they create a spherical ball having a diameter of 2 mm, or radius, r = 2/2 = 1 mm.

Hence, the volume of the resulting sphere is given by:

V = (4/3) x pi x r^3 = (4/3) x pi x 1^3 = 4.19 mm^3.

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