Volume of Sphere

This is a very simple article to show you how to calculate the volume given radius, and how to calculate the radius given the volume. The online calculator solver can also perform both of these calculations for you.

Formula

Here is the standard formula for calculating the volume given radius. A straightforward question is one where you have the radius and you simply plug the value into the equation above to calculate the answer.

How to calculate: You will need to use the cube function on your calculator, however if you do not have that then radius cubed is the same as "r × r × r". Then multiply the result by PI, which is 3.1415, then multiply by 4, and then divide the result by 3 to give the final answer.

If you have the diameter, and need to calculate the volume, then you simply divide the diameter by 2 to give radius.

Calculator Solver

Given radius, this online calculator will find the volume for you, however given the volume; it will find the radius for you.

Derivation Proof

The derivation of this formula will take a whole page of its own. I have an excellent article showing a proof by integration, which is ideal for students to understand. Please refer to the following article.

Volume of Sphere Derivation Proof

Find Radius

By transposing the previous formula, we obtain the formula to calculate the radius. Therefore, given the volume, this formula will calculate the radius. I have simply transposed it for calculating the radius. Transposition simply involves rearranging the terms for a different variable. It is a very easy thing to do and worth learning.

Units: If you have the volume in cubic centimetres then the radius will be in centimetres. If the volume is in cubic metres, then the radius will be in metres. If the volume is in cubic feet, then the radius will be in feet.

If the volume is in litres, then you will need to convert that into something useful. For example 1 litre = 1000 cm³, so multiply the volume by 1000 to convert. The radius r is then in centimetres.

Find Diameter

The formula above will give you an answer in terms of diameter. There is no need for a diameter calculator because all you have to do is to find radius and multiply that by 2 to find the diameter.

Finding the diameter from the radius is very simple. As you can see, the diameter is twice the radius. If you have the volume of a liquid sphere, and you need to calculate the diameter, then it is a simple matter of multiplying the radius by 2.

Question

A sphere has a radius r, which of the expressions below best represent the volume if r = 1.

a) 4 × PI / 3

b) 3 × PI / 4

c) 4

d) PI × 3 × 4

Answer: a