What is the formula for the volume of a sphere?

The formula for the volume of a sphere is \( V = \frac{4}{3} \pi r^3 \).

To understand this formula better, let's break it down. The letter \( V \) represents the volume of the sphere, which is the amount of space inside it. The symbol \( \pi \) (pi) is a mathematical constant approximately equal to 3.14159. The letter \( r \) stands for the radius of the sphere, which is the distance from the centre of the sphere to any point on its surface.

The formula \( V = \frac{4}{3} \pi r^3 \) tells us that to find the volume, we need to take the radius, cube it (multiply it by itself twice), then multiply by \( \pi \), and finally multiply by \(\frac{4}{3}\). This might seem a bit complex at first, but it’s just a series of straightforward steps.

For example, if you have a sphere with a radius of 3 cm, you would first cube the radius: \( 3^3 = 27 \). Then, you multiply this result by \( \pi \): \( 27 \times \pi \approx 84.823 \). Finally, you multiply by \(\frac{4}{3}\): \( \frac{4}{3} \times 84.823 \approx 113.097 \). So, the volume of the sphere would be approximately 113.097 cubic centimetres.

Understanding this formula is important because it helps you calculate the volume of any sphere, which is useful in many real-world situations, from finding the capacity of a spherical tank to understanding the properties of planets and stars.