Perhaps you already know how to calculate the volume of a cube or cone by taking some measurements and making the right calculations. But how much space does a fork or toy car take up? If you have to take measurements of an object, you can get them with the help of a container of water. If, on the other hand, you are struggling with a problem in your math book that describes an unusual form, read Method 2 on math problems to find out how to break them down into other, easier-to-solve problems.
Steps
Method 1 of 2: Finding the Volume of a Solid Object Using a Water Vessel
Step 1. Before starting, make sure the object is waterproof
This method involves immersing the object in water. If the object is hollow and not waterproof, you cannot use this method to measure the volume accurately. If the object absorbs water, make sure the liquid does not damage it, and read the instructions carefully to know how to adapt the procedure. Never immerse an electrical or electronic device, as it could cause a dangerous electric shock and / or damage the object without the possibility of repair.
If you can get hold of a vacuum sealer, you may want to seal a small object in a waterproof plastic liner that contains a minimal amount of air. This will allow you to get a good estimate of the volume, since the volume of the plastic used is probably relatively small compared to that of the object
Step 2. Find a vessel that can comfortably hold the object you want to measure
If it is a small object, you could use a graduated cylinder or measuring cup with the volume measurements printed on the side. Otherwise, find a waterproof container with an easy-to-calculate volume, such as a cylinder or rectangular box. A bowl will not give as accurate results, but you can consider it as a cylinder and get an approximate result, especially if, compared to the bowl, the object is very small.
It is also a good idea to keep a dry towel handy, as when you remove it from the container, the object will drip
Step 3. Fill the container with water, but only partially
Add enough water to submerge the object, but leave some space between the surface of the water and the top of the container. If the base of the bowl is irregular in shape, such as with rounded bottom corners, fill it enough so that it reaches a smoother part of the water, such as straight rectangular walls.
Step 4. Mark the water level
If the container is clear, mark the top of the water level on the outside with a water-erasable marker or other writing instrument that is easy to clean. Otherwise, mark the water level inside with a piece of colored tape or another tool, so that it cannot be washed by the water.
If you are using a graduated cylinder or a measuring cup that has the volume measurements on the side, you do not need to make any marks. Just look at the volume measurement on the surface of the water and note this number
Step 5. Drop the object into the bowl and see if it absorbs water
Immerse it completely. If it absorbs water, wait at least thirty seconds for it to fully absorb it, and then remove the object. The water level should have dropped, since some of the water has been absorbed by the object. Remove the mark or piece of colored tape, and replace it with another one indicating the new water level. Then dip the object back into the bowl and leave it there.
Step 6. Know what to do if the object floats
If the object floats, attach it to another dense, heavy object, and measure the volume of the two objects combined. After noting the result, repeat this method with the heavy object only to find its volume. Take the volume of the two combined objects (the first result) and subtract that of the heavy object. The result is the volume of the original object.
When measuring the volume of the heavy object alone, include in the measurement whatever you used to attach it to the original object, such as safety pins or tape
Step 7. Make a second mark at the new water level
If you are using a graduated cylinder or a measuring cup, you can just make a note of the indicated water level measurement. Once this is done, you can remove the object. It would be best not to leave it under water for more than a couple of minutes, since even "waterproof" objects can be damaged if left under water for too long.
Step 8. Understand why this method works
Since you know that when the object was submerged, the water level rose, the volume of the space between these two levels corresponds to the volume of the object. This is the displacement method and works on the principle that an object immersed in water displaces an amount of water equal to its volume. Depending on the type of vessel you used, there are different ways of calculating the volume of the displaced water (which is equivalent to that of the object). Finish solving the problem by continuing with the step that fits your vessel description.
Step 9. Find the volume using the measurements printed on the vessel
If you have used a graduated cylinder, a dispenser or any other container that shows the volume measurements on the side, you have already been able to write down the two volumes you need to calculate the answer. Take the volume you noted when the object was submerged (the largest volume) and subtract the volume of the original water level (the smallest volume). The answer you get corresponds to the volume of the object.
Step 10. Find the volume using a rectangular vessel
If you used a rectangular vessel, look at the space between the first and second marks you made to indicate the water levels. This space forms a "rectangular prism", or parallelepiped, which has been filled with the displaced water. Find the volume of this space by measuring the height between the two marks and the length and width of the inner surfaces of the vessel. As explained here, you can find the volume of this parallelepiped by multiplying its height, width and length (height x width x length) together. The result of this multiplication corresponds to the volume of the object.
- Do not measure the height of the entire vessel, but only the one between the two marks.
- Use this online calculator or look for another "rectangular prism calculator" that multiplies these numbers for you.
Step 11. Find the volume using a cylindrical vessel
If you used a cylindrical vessel, look at the space between the first and second marks you made to indicate the water levels. This cylindrical space is the one that had been filled by the displaced water, and, consequently, its volume corresponds to that of the object. To find the volume of this cylindrical space, you will need to take two measurements: height and diameter. First, measure the height between the two marks and write it down. Then find the diameter of the cylinder by measuring the distance between the two opposite inner walls of the cylinder, passing through the center. Then divide the diameter by two to find the radius, which is the distance from the center of the circle to the edge. Note the radius, then use the measurements to complete the calculation:
- Calculate πr2, or π x the radius x the radius, to find the area of the circle that forms the bases of the cylinder. If you don't have a calculator with the π key, find one online or make an approximation by replacing it with the value 3, 14.
- Multiply the result with the height between the two marks (which you measured at the beginning of this step) to find the volume of the space occupied by the water. This result corresponds to the volume of your object.
- To get a more precise result or to save yourself some calculations, you can enter your measurements into an online calculator for the volume of a cylinder.
Method 2 of 2: Calculate the Volume of an Irregularly Shaped Object in a Math Problem
Step 1. Break the object down into multiple regular shapes
If a math problem describes an irregularly shaped object and asks you to find its volume, you are probably expected to break it down. The math problem might give you some clues by describing the object, for example, as "a cone placed on top of a cube", or you may need to figure out from a diagram how to divide it into objects with shapes that are easier to measure.
Look for an anomalous angle (other than 90 degrees) in the irregular object. Can you "cut" it at that angle into two regular solids, like cylinders or pyramids? These solids do not necessarily have to have the same shape
Step 2. Write down the measurements of each section
To find the volume of a cube, rectangular prism or pyramid, you need to know its length, width and height. To find the volume of a cylinder or cone, you need to know its radius and height. Read the math problem carefully and write down the measurements of each section by marking them accurately or drawing a diagram of each section showing the measurements.
- If the problem tells you what the diameter is but not the radius, divide the diameter by two to find it.
- To find the measurements you need, you may need to do some addition or subtraction. For example, let's say the problem tells you that "a building that has the shape of a cone placed on top of a cube has a height of 30 units, but the height of the cube section is only 20 units". The height of the cone is not mentioned, but it is logical that it corresponds to 30 units - 20 units = 10 units.
Step 3. Calculate the volume of each section
To do this, use the most common formulas to find the volume of regular solids. Write down the result of each calculation and mark it, so you don't forget which section you have already calculated.
If you need a refresher on how to calculate volumes, see these instructions for the most common solids
Step 4. Add all the results together
After you calculate the volume of each individual section, add all the results together to get the volume of the entire object. Reread the math problem to make sure you haven't forgotten anything. If everything matches, congratulations - you have found the answer!
Advice
If you have a non-waterproof container and would like to measure the volume it can hold, fill it with small, identical objects that you know the volume of, such as small cubes of a certain size for sale in some school supplies stores. Count the number of small items needed to fill the bowl, then multiply them by the volume of a single item. Probably what you get will be an underestimate, since the objects will not be able to perfectly fill the entire space of the container (the smaller the objects, the more precise the result)
Warnings
- Objects that contain metal springs may run the risk of rusting, so be careful if this is the case.
- Permanent markers may leave marks that cannot be easily removed from any surface.
