There are many different ways to calculate the volume of an object, because every object has many different properties---such as mass, shape, and displacement---which relate back to its volume. Here are three different methods for finding volume. Depending on the object you are trying to measure, you will find that one method or another is preferable.
Solve for Volume by Space
All physical objects occupy space, and you can find the volume for some of them by measuring their physical dimensions. This is the easiest way to calculate the volume of objects with simple shapes, like cones, rectangular prisms, spheres, and cylinders.
For example, a honeydew melon is close enough in shape to a sphere that you can use the sphere equation to calculate its volume and still get a fairly accurate answer.
There is a link in the Resources section to a NASA website which provides volume equations for various simple shapes, and a few not-so-simple ones.
Solve for Volume by Density and Mass
Density is defined as an object's mass per a given unit of volume. So, if you know the object's density, and you're able to weigh it, you can determine its volume with the equation:
Volume = weight / density
There is a link in the Resources section to a webpage which lists the densities of some common materials. Note that density changes with pressure or temperature.
Solve for Volume by Displacement
This is another way of measuring the physical space that an object occupies. If the object has an abnormal shape, you might be unable to measure its physical dimensions accurately. Instead, what you can do is measure the volume which is displaced when the object is immersed in a liquid or a gas. This is a very common method for measuring volume, and when done correctly, it is highly accurate.
For example, if you want to know the volume of a piece of ginger root, you can fill a beaker or a measuring cup with a known volume of water---let's say one cup. Next, add the ginger. Make sure that it is submerged underwater. Then, measure the new volume at the water line. The new volume will always be more than the starting volume. Subtract the starting volume (one cup) from this new volume, and you will have the volume of the ginger.
Avoid a Common Mistake
If the surface of an object is not what mathematicians call "closed," then its true volume may be different from what you would expect. For instance, a drinking glass which holds one pint is hollow in the middle and doesn't have a top, which means that it doesn't have a closed surface. So, if you think of it as being generally cylindrical in shape, you would be mistaken: Its cross-section is not a rectangle with an enclosed area, as would be the case with a cylinder, but more of a horseshoe shape that has no enclosed area. The drinking glass will hold one pint of soda, but it doesn't actually have one pint of volume. Its volume consists only of the actual glass, which is much less than a pint. When measuring volumes, be on the lookout for these kinds of shapes with "open" surfaces. They are tricky.