Volume of Sphere Formula

Volume of Sphere Formula

Formula

Summary

The volume of a sphere is given by two-thirds multiplied by the circle constant (tau) multiplied by the radius cubed.

Variable Description
The volume of the sphere.
The radius of the sphere, where the radius is measured from the center of the sphere to any point on its surface.
The circle constant (tau), where the value of is approximately .
Note: This website uses the constant (tau) instead of (pi) as the default circle constant. The substitution can be used to translate between the two constants.

Usage

The volume of a sphere is equal to two-thirds multiplied by the circle constant (tau) multiplied by the radius cubed. For example, to calculate the volume of a sphere with a radius of the formula is:

Raise to the power which is equal to .

Simplify the expression.

The volume of the sphere with a radius of is equal to units cubed. To calculate an approximate value for the sphere, substitute into the expression and multiply.

Examples

Example 1

Volume of Sphere Example

This example demonstrates how to calculate the volume of a sphere with a radius equal to .

Steps

  1. Set up the volume for a sphere formula.

  2. Substitute the radius into the equation.

  3. Evaluate the exponent expression.

    The volume of the sphere is equal to cube units or approximately cube units.

Example 2

Volume of Sphere radius 2 Example

This example demonstrates how to calculate the volume of a sphere with a radius equal to .

Steps

  1. Set up the volume for a sphere formula.

  2. Substitute the radius into the equation.

  3. Evaluate the exponent expression and combine like terms

    The volume of the sphere is equal to cube units or approximately cube units.

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