Q&A for How to Calculate the Volume of an Irregular Object

If it's an irregular solid shape, take a measuring cylinder and add water. Measure the volume of water in the cylinder as v1. Then put the irregular solid in the cylinder and measure its volume as v2. To find the volume: (v2-v1)

See Method 1 above.

Cylinders come in lots of sizes. Use one slightly larger than the object.

You would use the water-displacement method shown above, but there would be three obstacles. You would first have to determine that the air valve will not let water into the ball. Then, because deflated basketballs always have some air inside them, thereby causing the ball to float in water, you would have to force the ball below the water's surface, and whatever you use to hold the ball below the surface would add to the ball's volume. You would have to use something like a very small stick. Even that would affect the volume measurement a little. Thirdly, for complete accuracy, you would want to remove air bubbles attached to the surface of the ball. You could use your hands to do that.

Method 1 above is called "water displacement." Method 2 doesn't have a name.

If you are trying to find the volume of a very small object, you will need to use a tiny container, such as a very small graduated cylinder designed for this task.

You can find the volume using water displacement. Measure a volume of water. Drop the object into the water, and measure the difference. 1 ml = 1 cm3

In the case of a land mass, the easiest way would be to learn (or calculate) the average elevation above sea level of the entire land mass, and multiply that by the surface area of the land mass. You'd have to define the land mass as everything above sea level, even though the entire mass is attached to (and a part of) the Earth's crust.

Use a weight to submerge the object in the water. Find the water displacement as described above. Then find the volume of the weight (by water displacement or by mathematics), and subtract that from the full water displacement.

Drop the object into a marked beaker of water and see how water is displaced.

Because the more irregular the shape, the harder it is to calculate its volume mathematically.

There is no "best" unit. The most appropriate unit depends on the size of the object. A very small object could be measured in cubic millimeters. Larger objects might be measured in cubic centimeters, inches, feet, yards, or meters.

Yes. That is a variation of the water displacement method.

The fact that the object is "irregular" means that it is not subject to mathematical measurement and analysis. If you happen to know the exact density of the object, you could weigh it and divide the weight by the density. Otherwise, you're limited to water displacement.

You would have to use the water-displacement method, using water just above the freezing point. You'd have to do it quickly so that the ice cube doesn't melt much. The volume you'd get would be only approximate, because some melting would be unavoidable.

One possibility is to shrink-wrap the object before immersing it in the water. Another possibility is to use oil, a thin gel substance or fine-textured sand in the container instead of water.

The most accurate method is to evaluate a double integral knowing a function for the bowl.