Volume is the amount of space contained within a threedimensional object. Shapes such as spheres, prisms, and cylinders are threedimensional objects that take up a certain amount of space, which we can call its volume. We measure volume in cubic units. Here are some examples of cubic measurements:

cubic meters  

cubic feet  

cubic kilometers 
With these measurements, we can easily tell they are cubic measurements because they include an exponent of three. Not all cubic measurements have this visual clue. For example, the liter is abbreviated with the letter L, and does not contain an exponent of three, yet it is a cubic measurement (it measures liquid volume, and is actually equivalent to 1000 cubic centimeters).
There are several formulas for finding the volumes of different shapes. We are going to focus on the volumes of a rectangular prism, cylinder, and sphere. Here are the formulas to know:
Take a look at the figure below:
To find the volume, we simply multiply all of the dimensions together. This includes the units of measurement.
Let's use a formula to find the volume of a cylinder:
To find the volume, first we square the radius of the circular base, and then we multiply by pi and the height. Remember that the order of operations dictates exponents before multiplication, so that's why we square the radius before multiplying anything.

Formula for the volume of a cylinder  

Substitute radius length and height  

Square the radius  

Multiply by 4 inches  

Our Solution, using 
Notice that some of these formulas include the number, pi. Pi is an important number.
Let's find the volume of the sphere pictured below:
The only piece of information we are given is the radius of the sphere, but this is all we need to calculate the volume. Just like with the volume of a cylinder, first we apply the exponent. After cubing the radius, we multiply it by pi and then by fourthirds.

Formula for the volume of a sphere  

Substitute radius length  

Cube the radius  

Multiply by  

Our Solution, using 
In our previous examples, we used given measurements for side lengths and radii to calculate the volume of a threedimensional object. In the following examples, we are going to use a given measurement of volume to calculate a side length or a radius. We will use the same formulas, but in a different way.
We'll start with finding the side length of a rectangular prism:
Dividing both sides of the equation by the length and the height will do two things: first, it will cancel the length and the width from one side of the equation, leaving just an expression for the width.
Second, it can help us cancel the cubic units on the other side if the equation, leaving our answer in linear centimeters. (Linear centimeters just means regular centimeters we are used to measure. We would only say "linear" if we wanted to make it clear that it isn't square centimeters or cubic centimeters.)
Now we can perform the numeric division on the left side of the equation. This is our solution for the width of the prism:

Divide volume by length and height  

Simplify denominator  

Our Solution 
Lastly, let's use a volume formula to solve for an unknown radius. Consider the sphere below:
We are given the volume as 65.45 cubic inches, with an unknown radius. Substituting known information into the formula for the volume of a sphere, we have:
How can we isolate r? Look at the numbers and operations surrounding the variable r. It is being raised to the power of 3, and then multiplied by (4/3)pi. We need to undo this by applying inverse operations, but also in reverse order. This means first we need to undo the multiplication by (4/3)pi, and then undo the power of 3.

Divide both sides by  

Units have not changed  

Apply the cube root of both sides  

Our Solution 