The formula for the volume of a sphere is given by V = \frac{4}{3} \pi r^3, where V represents the volume and r is the radius of the sphere.
To explain further, the volume of a sphere measures the amount of space enclosed within it. The constant \pi (approximately 3.14159) is used to relate the sphere’s geometry to its volume. The r^3 indicates that you take the radius and cube it, meaning you multiply the radius by itself three times. Multiplying this result by \frac{4}{3} gives you the total volume of the sphere.
This formula is derived from calculus, specifically through integration, but it can be understood intuitively by considering how spheres occupy space in three dimensions. So, whenever you need to calculate the volume of a sphere, simply measure its radius and plug it into the formula!