How to Calculate the Volume of a Sphere

The volume of a sphere refers to the amount of space inside the three-dimensional object. In real-world terms, if you filled up a spherical object with a liquid, the volume would represent the quantity of liquid the sphere can hold. To calculate the volume of a sphere, there are two main formulas, depending on whether you know the radius or the diameter of the sphere.

In this guide, we'll explain how to calculate the volume of a sphere step by step using both the radius-based formula and the diameter-based formula. Additionally, we’ll provide calculators below to help you quickly compute the volume.

Formula to Calculate the Volume of a Sphere Using the Radius

The most common way to calculate the volume of a sphere is to use the formula that requires the radius. The radius is the distance from the center of the sphere to any point on its surface.

The Radius-Based Formula

The formula to calculate the volume of a sphere using the radius is:

V = (4/3) * π * r³

Where:

• V is the volume of the sphere.
• r is the radius of the sphere.
• π (Pi) is a constant approximately equal to 3.14159.

Step-by-Step Explanation Using Radius

To better understand how to calculate the volume of a sphere, let's walk through a step-by-step process with a concrete example:

1. Step 1: Measure or obtain the radius (r) of the sphere. For example, let's say the radius is 6 cm.
2. Step 2: Use the formula V = (4/3) * π * r³.
3. Step 3: Cube the radius. This means multiplying the radius by itself three times. For a radius of 6 cm:
   6³ = 6 * 6 * 6 = 216.
4. Step 4: Multiply the cubed radius by π (Pi ≈ 3.14159) and 4/3.
   V = (4/3) * π * 216 ≈ (4/3) * 3.14159 * 216
5. Step 5: Calculate the result:
   V ≈ 4.18879 * 216 ≈ 904.78 cm³.

So, the volume of a sphere with a radius of 6 cm is approximately 904.78 cm³.

This method is the most commonly used to calculate the volume of a sphere, especially in school problems or practical geometry tasks.

Formula to Calculate the Volume of a Sphere Using the Diameter

If the diameter of the sphere is given instead of the radius, you can still calculate the volume of the sphere. The diameter is simply twice the radius, so you can adjust the formula accordingly.

The Diameter-Based Formula

The formula to calculate the volume of a sphere using the diameter is:

V = (π/6) * d³

Where:

• V is the volume of the sphere.
• d is the diameter of the sphere.

Step-by-Step Explanation Using Diameter

Let's go through a step-by-step process for calculating the volume using the diameter:

1. Step 1: Measure or obtain the diameter (d) of the sphere. For this example, let's say the diameter is 12 cm.
2. Step 2: Use the formula V = (π/6) * d³.
3. Step 3: Cube the diameter. For a diameter of 12 cm:
   12³ = 12 * 12 * 12 = 1728.
4. Step 4: Multiply the cubed diameter by π/6. This means:
   V = (π/6) * 1728 ≈ (3.14159/6) * 1728.
5. Step 5: Calculate the result:
   V ≈ 0.5236 * 1728 ≈ 904.78 cm³.

So, the volume of a sphere with a diameter of 12 cm is also approximately 904.78 cm³.

Conclusion

Whether you are given the radius or the diameter, calculating the volume of a sphere is straightforward if you use the appropriate formula. Both methods will lead to the same result, so it's important to understand the relationship between the radius and the diameter. The formulas are simple, and once you know either the radius or the diameter, you can easily calculate the volume of any sphere.

For a quick calculation, you can use the following calculators. One allows you to input the radius, and the other works with the diameter.