How to Calculate the Volume of a Sphere

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A sphere is a perfect three-dimensional circular object, each point on its surface having an equal distance from the center of the sphere. In life, there are many common objects that are spherical like balls, globes, and so on. If you want the volume of a sphere, you need to find its radius, then apply the radius to the simple formula, V = ⁴⁄₃πr³.

Table of Contents

Steps

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Write down the formula for the volume of a sphere. We have: V = ⁴⁄₃πr³ . Where, “V” represents the volume and “r” is the radius of the sphere.

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Find the radius. If there is a radius available then we can take the next step. And if the problem gives you the diameter, to find the radius you just need to divide the diameter in half. Once you have the data, write it down on paper. For example, we have a sphere radius of 1 cm. ^{[1] X Research Source}

If you only have the area of the sphere (S), to find the radius, divide the area of the sphere by 4π, and then calculate the square root of this result. That is, r = √(S/4π) (“radius is the square root of the quotient of the area and 4π”).

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Calculate the third power of the radius. To do this, simply triple the radius by itself or raise it to the power of three. For example, (1 cm) ³ is actually 1 cm x 1 cm x 1 cm. The result of (1 cm) ³ is still 1 because 1 multiplied by itself is still 1. You will have to rewrite the unit of measure (centimeter here) after giving your answer. . When the calculation is complete, you substitute the value r³ into the original formula for the volume of the sphere, V = ⁴⁄₃πr³ . In this example, we have V = ⁴⁄₃π x 1 .

For example, if the radius is 2 cm, after the radius is raised to the third power we have 2 ³ , which is 2 x 2 x 2 or 8.

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Multiply the third power of the radius by 4/3. Substitute r ³ , or 1, into the formula V = ⁴⁄₃πr³ , then continue to multiply to make the equation more compact. 4/3 x 1 = 4/3. Now, our formula will be V = ⁴⁄₃ x π x 1, or V = ⁴⁄₃π.

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Multiply the expression by π. This is the final step to find the volume of the sphere. You can leave π in the answer as V = ⁴⁄₃π. Or, you put π into the calculation and multiply its value by 4/3. The value of π is equivalent to 3.14159, so V = 3.14159 x 4/3 = 4.1887, you can round to 4.19. Don’t forget to conclude with the unit of measure and return the result to cubic units. So, the volume of a sphere with radius 1 is 4.19 cm ³ .

Advice

Don’t forget to use cubic units (e.g. 31 cm³ ).
Make sure that the quantities in the problem have the same units of measure. If not, you will have to convert them.
Note, the symbol “*” is used as a multiplication sign to avoid confusion with the variable “x”.
If you want to calculate a part of a sphere, such as a half or a quarter, first find the total volume, and then multiply that volume by the fraction you are looking for. For example, a sphere has a total volume of 8, to find the volume of a half sphere, you have to multiply 8 by ½ or divide 8 by 2, the result is 4.

Things you need

Calculator (reason: for complex calculations)
Pencil and paper (not necessary if you have an advanced computer)

Steps

Advice

Things you need

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