How to find the Volume of a Sphere in 4 Easy Steps

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How to find the Volume of a Sphere | Mathcation

Key Points about Volume of a Sphere

  • The volume of a sphere is a fundamental concept in geometry that is used in various fields.
  • The formula for calculating the volume of a sphere is (4/3) x pi x r³, where r is the radius of the sphere.
  • The volume of a sphere can also be calculated using the circumference of the sphere.

A Short Explanation for finding the Volume of a Sphere

Finding Volume of a Sphere can be completed easily by using the formula and following correct order of operations. The first step in finding Volume of a Sphere is understanding that you are cubing the radius of the sphere first. Be sure to remember that the radius is equal to half of the diameter. Once you cube the radius, you must multiply by four times pi. Next, you divide the solution by three. The final step for finding Volume of a Sphere is to follow order of operations and simplify the equation.

The volume of a sphere is a fundamental concept in geometry that is used in various fields, including physics, engineering, and architecture. A sphere is a three-dimensional shape that is completely round, with all points on its surface equidistant from the center. Finding the volume of a sphere is essential in the calculation of the amount of space it occupies.

The formula for calculating the volume of a sphere is (4/3) x pi x r³, where r is the radius of the sphere. If the diameter of the sphere is given instead of the radius, it is necessary to divide the diameter by 2 to obtain the radius. The volume of a sphere can also be calculated using the circumference of the sphere. By measuring the circumference of the sphere, one can determine the radius and then use the formula to calculate the volume.

Common Core Standard: 8.G.C
Related Topics: Pythagorean Theorem, Parallel Lines Cut by a Transversal, Triangle Angle Sum, Exterior Angle of a Triangle, Volume of a Cylinder, Volume of a Cone
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How to find the Volume of a Sphere

Volume of a Sphere Formula: How to Use

The volume of a sphere is the amount of space occupied by the sphere. It is measured in cubic units, such as meters cubed (m³), centimeters cubed (cm³), or inches cubed (in³). The formula for calculating the volume of a sphere is derived from the geometry of a sphere.

The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159. The cube root of the volume formula is used to calculate the radius of the sphere.

Calculating the volume of a sphere is a straightforward process. First, measure the radius of the sphere. If the radius is not known, the circumference of the sphere can be measured instead, and the radius can be calculated using the formula r = circumference / (2π). Once the radius is known, the volume of the sphere can be calculated using the formula V = (4/3)πr³.

A sphere volume calculator can be used to perform the calculations for you. Simply input the radius of the sphere into the calculator, and it will output the volume of the sphere in the desired units.

In summary, the formula for the volume of a sphere is V = (4/3)πr³, where V is the volume, r is the radius, and π is a mathematical constant. The volume of a sphere can be calculated using the formula or by using a sphere volume calculator.

 

How to find the Volume of a Sphere with Diameter

To calculate the volume of a sphere given its diameter, you first need to determine the radius of the sphere. The radius is half the diameter, so you can simply divide the diameter by 2 to get the radius. Once you have the radius, you can use the formula for the volume of a sphere, which is:

V = (4/3)πr³

Where V is the volume and r is the radius.

To make things easier, you can use an online sphere volume calculator like the one found here. All you need to do is enter the diameter of the sphere, and the calculator will give you the volume.

If you prefer to do the calculation by hand, you can use the following steps:

  1. Divide the diameter by 2 to get the radius.
  2. Cube the radius (multiply it by itself three times).
  3. Multiply the result by 4/3.
  4. Multiply the result by π.

Here’s an example:

Suppose you have a sphere with a diameter of 6 cm. To find the volume, you first need to find the radius:

r = d/2 = 6/2 = 3 cm

Next, you need to cube the radius:

r³ = 3³ = 27

Then, you can multiply by 4/3:

(4/3) × 27 = 36

Finally, you can multiply by π:

36 × π ≈ 113.1

So the volume of the sphere is approximately 113.1 cubic centimeters.

 

How to find the Volume of a Sphere Solution

3 Simple Volume of a Sphere Examples

To better understand the concept of the volume of a sphere, let’s take a look at some examples.

  1. In order to solve for Volume of a Sphere you must know that the volume is equal to the radius cubed, times pie, times four, and then divided by three.
  2. The radius is equal to a half of the spheres diameter.
  3. You substitute in the radius of the sphere for r.
  4. Cube the radius.
  5. Multiply times pi.
  6. Multiply times four.
  7. Finally divide by three and be sure to use the correct units.

Example 1

What is the volume of a sphere with a radius of 5 cm?

Using the formula for the volume of a sphere, V = 4/3 π r³, we can plug in the given radius and solve for the volume:

V = 4/3 × π × 5³ V = 523.6 cm³

Therefore, the volume of the sphere is 523.6 cubic centimeters.

Example 2

A spherical water tank has a radius of 2 meters. What is the volume of water it can hold?

Again, we can use the formula for the volume of a sphere to find the answer:

V = 4/3 × π × 2³ V = 33.5 m³

Therefore, the spherical water tank can hold 33.5 cubic meters of water.

Example 3

A metal sphere has a volume of 288π cubic centimeters. What is its radius?

We can rearrange the formula for the volume of a sphere to solve for the radius:

V = 4/3 × π × r³ r = (3V/4π)^(1/3)

Plugging in the given volume, we get:

r = (3 × 288π/4π)^(1/3) r = 6 cm

Therefore, the metal sphere has a radius of 6 centimeters.

These examples demonstrate how the formula for the volume of a sphere can be used to solve a variety of problems involving spheres.

 

5 Quick Volume of a Sphere Practice Problems

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Volume of a Sphere Quiz

Click Start to begin the practice quiz!

1 / 5

Find the volume of the sphere.

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2 / 5

Find the volume of the sphere.

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3 / 5

Find the volume of the sphere.

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4 / 5

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5 / 5

Find the volume of the sphere.

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Your score is

0%

 

Volume of a Sphere Equation: Radius, Diameter, and Circumference

The volume of a sphere is the amount of space occupied by a sphere. It is measured in cubic units. The formula for calculating the volume of a sphere is:

V = (4/3) × π × r³

where V represents the volume and r represents the radius of the sphere.

To calculate the volume of a sphere, you need to know the value of r. If you are given the diameter of the sphere, you can calculate the radius by dividing the diameter by 2.

r = d/2 

where d represents the diameter of the sphere. Once you have the value of r, you can substitute it into the formula to calculate the volume of the sphere.

V = (4/3) × π × r³

It is important to note that the value of π is a constant that is approximately equal to 3.14.

The formula for the volume of a sphere can also be written in terms of the sphere’s circumference. If you know the circumference of the sphere, you can calculate the radius using the following formula:

r = C / (2 × π)

where C represents the circumference of the sphere. Once you have the value of r, you can substitute it into the formula to calculate the volume of the sphere.

V = (4/3) × π × r³

In summary, the volume of a sphere can be calculated using the formula V = (4/3) × π × r³, where V represents the volume and r represents the radius of the sphere. The formula can also be written in terms of the sphere’s diameter or circumference.

 

How to Find the Volume of a Sphere FAQ

How do you find the volume of a sphere?

To find the volume of a sphere, you need to know its radius. The formula for the volume of a sphere is V = 4/3 π r³, where V is the volume and r is the radius. Once you have the radius, you can plug it into the formula to find the volume of the sphere.

What is the formula for the volume of a sphere?

The formula for the volume of a sphere is V = 4/3 π r³, where V is the volume and r is the radius. This formula can be used to find the volume of any sphere, regardless of its size.

Why is the volume of a sphere 4/3 π r³?

The volume of a sphere is 4/3 π r³ because a sphere is a three-dimensional shape with no edges or vertices. That means its points lie in space, and the volume of the sphere is the amount of space it occupies.

What does 4/3 mean in the volume of a sphere?

The 4/3 in the volume of a sphere formula represents the ratio of the volume of a sphere to the volume of a circumscribed cube. In other words, if you were to put a sphere inside a cube so that the sphere touches all six faces of the cube, the volume of the sphere would be 4/3 times the volume of the cube.

How to calculate volume of a sphere?

To calculate the volume of a sphere, you need to know its radius. Once you have the radius, you can use the formula V = 4/3 π r³ to find the volume of the sphere.

How do you find the volume of a ball with the diameter?

To find the volume of a ball with the diameter, you first need to find the radius by dividing the diameter by 2. Once you have the radius, you can use the formula V = 4/3 π r³ to find the volume of the ball.

How To Calculate the Volume of Sphere With Diameter?

To calculate the volume of a sphere with diameter, you first need to find the radius by dividing the diameter by 2. Once you have the radius, you can use the formula V = 4/3 π r³ to find the volume of the sphere.

 

Volume of a Sphere Worksheet: Video Explanation

Watch our free video on How to find the Volume of a Sphere. This video shows how to solve problems that are on our free Volume of a Sphere worksheet that you can get by submitting your email above.

Watch the free How to find the Volume of a Sphere video on YouTube here: How to find the Volume of a Sphere

Video Transcript:
This video is about how to find the volume of sphere and in order to show you how to find the volume of a sphere we’re gonna use our volume of sphere worksheet that you can get on our website. These practice problems will help you with the formula for volume of a sphere and answering how to find volume of a sphere.

We’re gonna do a couple practice problems on the sphere volume worksheet. The first practice problem is a sphere that has a radius of 4 inches. Now in order to find the volume of sphere you have to use the volume of a sphere formula which is 4 PI R cubed divided by 3. In order to simplify this formula you have to find the piece that is missing, which is the radius.

Now in the case of this example our radius is 4 and once we know our radius we will take our radius and we will substitute it in to our volume of a sphere formula. This is the volume of a sphere formula missing the radius and in this case the radius is 4 so we’re gonna substitute that in for R. Once we put this into our calculator and simplify the volume is going to be 268.08 inches cubed this will give you the sphere volume.

Our next problem is a little bit different because instead of giving us the radius they give us the diameter. It throws in a curve ball for using the volume of sphere equation to learn how to find volume of sphere. In order to figure out how to find the volume of this sphere what we’re going to do is we’re going to use our volume of sphere formula.

Volume equals 4 PI R cubed divided by 3 and we still have to find the radius, but this time they don’t give us the radius they give us a diameter, which is the entire length of the circle inside the sphere.

What that means is I want to find the radius and the radius is half of the diameter. We will take our diameter and divide it by 2,  24 divided by 2 is 12. We’re going to use 12 to substitute in for the radius. Volume will be 4 times pi times the radius cubed which is 12/3.

After we put all this into our calculator we will get seven thousand two hundred and thirty eight point twenty three feet cubed because that is our unit. This is the easiest way to use the sphere volume formula. You can download the free volume of spheres worksheet above.

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Free Volume of a Sphere Worksheet

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