In order to determine the density of a substance, it is necessary to divide the mass of the body by its volume:
Body weight can be determined using scales. How to find the volume of a body?
If the body has the shape of a rectangular parallelepiped (Fig. 24), then its volume is found by the formula
V = abs.
If it has some other form, then its volume can be found by the method that was discovered by the ancient Greek scientist Archimedes in the 3rd century BC. BC e.
Archimedes was born in Syracuse on the island of Sicily. His father, the astronomer Phidias, was a relative of Hieron, who became in 270 BC. e. the king of the city in which they lived.
Not all of Archimedes' writings have come down to us. Many of his discoveries became known thanks to late authors, whose surviving writings describe his inventions. So, for example, the Roman architect Vitruvius (I century BC) in one of his writings told the following story:
“As for Archimedes, of all his numerous and varied discoveries, the discovery that I will tell about seems to me made with boundless wit. 
During his reign in Syracuse, Hiero, after the successful completion of all his activities, made a vow to donate a golden crown to the immortal gods in some temple. He agreed with the master about great price for the work and gave him the weight of gold he needed. On the appointed day, the master brought his work to the king, who found it excellently executed; after weighing, the weight of the crown was found to correspond to the given weight of gold.
After that, a denunciation was made that part of the gold was taken from the crown and the same amount of silver was mixed in instead. Hiero was angry that he had been tricked, and, not finding a way to convict this theft, asked Archimedes to think carefully about it. He, immersed in thoughts on this issue, somehow accidentally came to the bathhouse and there, sinking into the bath, noticed that such an amount of water was flowing out of it, what was the volume of his body immersed in the bath. Finding out for himself the value of this fact, he, without hesitation, jumped out of the bath with joy, went home naked and in a loud voice let everyone know that he had found what he was looking for. He ran and shouted the same thing in Greek: “Eureka, Eureka! (Found, found!)
Then, Vitruvius writes, Archimedes took a vessel filled to the brim with water and lowered into it a gold ingot equal in weight to a crown. After measuring the volume of water displaced, he again filled the vessel with water and lowered the crown into it. The volume of water displaced by the crown turned out to be greater than the volume of water displaced by the gold ingot. The larger volume of the crown meant that it contained a substance less dense than gold. Therefore, the experiment done by Archimedes showed that part of the gold was stolen.
So, to determine the volume of a body having irregular shape, it is enough to measure the volume of water displaced by a given body. With a measuring cylinder (beaker), this is easy to do.
In cases where the mass and density of the body are known, its volume can be found by the formula following from formula (10.1):
From here it is clear that To determine the volume of a body, divide the mass of the body by its density..
If, on the contrary, the volume of the body is known, then, knowing what substance it consists of, you can find its mass:
m = ρV. (10.3)
To determine the mass of a body, it is necessary to multiply the density of the body by its volume.
1. What methods of volume determination do you know? 2. What do you know about Archimedes? 3. How can you find the mass of a body by its density and volume?
Experimental task. Take a bar of soap that has the shape of a rectangular parallelepiped, on which its mass is indicated. After making the necessary measurements, determine the density of the soap.
Content:
Volume is the amount of space a body occupies, and density is the mass of a body divided by its volume. Before calculating the density of a body, it is necessary to find its volume. If the body has the correct geometric shape, its volume can be calculated using a simple formula. Volume is usually measured in cubic centimeters (cm 3) or cubic meters(m 3). Using the found volume of the body, it is easy to calculate its density. Density is measured in grams per cubic centimeter (g/cm3) or grams per milliliter (g/ml).
Steps
Part 1 Calculating the Volume of a Regularly Shaped Body
- 1
Determine the shape of the body. Knowing the form will allow you to choose correct formula and take the measurements needed to calculate the volume.
- Sphere is a perfectly round three-dimensional object, all points of the surface of which are separated by equal distance from the center. In other words, a spherical body is like a round ball.
- Cone- This is a three-dimensional figure, at the base of which lies a circle, and the top is a single point, called the top of the cone. A cone can also be represented as a pyramid with a round base.
- Cube is a three-dimensional figure composed of six identical square faces.
- cuboid, also called a rectangular prism, is similar to a cube: it also has six faces, but in this case they are rectangles, not squares.
- Cylinder is a three-dimensional figure consisting of identical round ends, the edges of which are connected by a rounded surface.
- Pyramid is a three-dimensional figure, at the base of which lies a polygon, which is connected to the top by side faces. Correct pyramid a pyramid is called, at the base of which lies regular polygon, all sides and angles of which are equal to each other.
- If the body has an irregular shape, its volume can be found by completely submerging it in water.
- 2
Choose the correct equation to calculate the volume. Each type of body has its own formula that allows you to calculate the volume it occupies. Below are the formulas for finding the volume of the figures listed above. More details and illustrations can be found in the article.
- Sphere: V = (4/3) π r 3, where r is the radius of the sphere and π is a constant of about 3.14.
- Cone: V = (1/3) π r 2 h, where r is the radius of the round base, h is the height of the cone, π is a constant equal to approximately 3.14.
- Cube: V = s 3, where s is the length of the edge of the cube (the side of any of its square faces).
- cuboid: V = lxwxh, where l is the length rectangular face, w is its width, h is the height of the parallelepiped (prism).
- Cylinder: V= π r 2 h, where r is the radius of the round base, h is the height of the cylinder, π is a constant of approximately 3.14.
- Pyramid: V= (1/3) b x h, where b is the area of the base of the pyramid (l x w), h is the height of the pyramid.
- 3
Take the necessary measurements. They will depend on what kind of body you are dealing with. For most simple shapes, you will need to measure the height; if the figure has a round base, it is also necessary to determine its radius; if the base is a rectangle, its length and width.
- The radius of a circle is half its diameter. Measure the diameter by placing a ruler in the middle of the circle, then divide the result by 2.
- The radius of a sphere is a little more difficult to measure, but it's not difficult if you use the methods detailed in the article.
- The length, width and height of a body can be determined by placing a ruler on the body at the appropriate places and recording the measurements.
- 4
Calculate volume. Having found out the shape of the body, select the appropriate formula and measure the quantities included in it. Substitute the measured values into the formula and perform the necessary mathematical operations. As a result, you will get the volume of the body.
- Remember that the answer must be expressed in cubic units, regardless of which system of units you use (metric or otherwise). After the received value, be sure to write the units in which it is measured.
Part 2 Calculating the Volume of an Irregular Body
- 1
Determine the volume of a body by the amount of water it displaces. The body may have an irregular shape, which makes it difficult to measure its dimensions and leads to an inaccurate determination of volume. In this case, the method works perfectly, which consists in determining the volume of water displaced by the body when completely immersed.
- This method can also be applied to find the volume of bodies of the correct form in order to avoid calculations.
- 2
Fill the measuring cylinder (beaker) with water. This is a laboratory container with marks on the side surface, which allows you to measure the volume of liquids. Select a cylinder large enough to completely fit the object to be measured. It is necessary to fill the cylinder with water so that the object can be completely immersed in it, but it does not spill out. Record the initial volume of water without the measured body.
- Observing the initial volume of water, bend down so that your eyes are level with the surface of the liquid, and then record the height at which the bottom of the meniscus is located. The meniscus is the outer surface of the water, which curves when in contact with other surfaces (in our case, these are the walls of the vessel).
- 3
Gently place the body to be measured into the container. Do this slowly so as not to drop the object, as this may cause some of the water to splash out of the graduated cylinder. Make sure the body is completely submerged in water. Record the new reading of the water level in the container, again positioning yourself so that your eyes are at the same level as the meniscus.
- If some of the water splashes out while immersing the body, try again from the very beginning, pouring less water or taking a larger graduated cylinder.
- 4
Subtract from the final water level its original value. The amount of water displaced by the object will be equal to its volume in cubic centimeters. Usually the volume of liquids is measured in milliliters, but one milliliter is exactly equal to one cubic centimeter.
- For example, if at first the water level was 35 ml, and after lowering the object into it, it rose to 65 ml, the volume of this object is 65 - 35 \u003d 30 ml, or 30 cm 3.
Part 3 Density calculation
- 1
Determine the mass of the object. The mass of an object corresponds to the amount of matter of which it is composed. The mass is found by direct weighing on the balance, it is measured in grams or kilograms.
- Take an accurate measuring scale and place an object on it. Record the scale readings in your notebook.
- Body weight can also be determined using a weighing scale. After placing the object on one bowl, on the second place the weights with known masses so that both bowls balance each other, located on the same height. In this case, the desired mass of the object will be equal to the sum of the masses of the weights used.
- Before weighing, make sure that the object is not wet, otherwise the measurement error will increase.
- 2 Determine the volume of the body. If the object has the correct shape, use one of the formulas above to determine its volume. If the shape of the body is not correct, measure the volume by immersing it in water as described above.
- 3
Calculate the density. By definition, density is equal to mass divided by volume. Thus, divide the measured mass by the calculated volume. As a result, you will get the density of the body, measured in g / cm 3.
- For example, let's calculate the density of an object with a volume of 8 cm 3 and a mass of 24 g.
- density = mass / volume
- d \u003d 24 g / 8 cm 3
- d \u003d 3 g / cm 3
- Often objects consist of several parts that have the correct geometric shapes. In this case, divide the constituent elements into groups related to one or another correct form, find the volume of each element, and then add them together, thereby determining the total volume of the entire object.
- You can determine the volume of an object both by calculations and by immersion in water, and then compare the results.
Warnings
- Be careful: before proceeding with the calculations, be sure to convert all measured values to metric system(SI system of units).
The number of boxes
Result:
The volume of one box (m 3):
Total volume (m 3):
Use received
result for
application form
| d= | m cm | |
| h= | m cm |
Number of pipes
Result:
The volume of one pipe (m 3):
Total volume (m 3):
Use received
result for
application form
How to calculate the volume of a box?
Do you have a question about delivery?, and also there was a need to know how to calculate the volume of cargo, do you need our help? We know how to calculate the volume of cargo, on this page you see a calculator that will accurately perform the calculations.
In general, for what purpose is the volume calculated?
It is necessary to calculate the volume in order to avoid misunderstandings when loading loaded boxes into vehicle. Calculate the volume using modern technologies today it is not difficult, your being here is enough.
What criteria do we use to calculate the volume of cargo?
Firstly, everyone knows that every detail is important in the delivery process, and it is important to calculate the volume of cargo as a whole without errors. As already mentioned, our volume calculator will help you calculate the volume of cargo, it will do it quickly and reliably!
Second- volume calculator, start it on our website, already mentioned above, as you can see, we care about our customers. The volume calculator, that's what can make it as easy as possible to work with calculations, and completely kill your doubts.
What are we giving you?
What else is needed?
For example…
You are an entrepreneur who is engaged in transportation from China, and you constantly need a calculator for calculating the volume. You can quickly find the volume calculator on the pages of our website, and perform your calculations right now.
Nowadays, business is based on the Chinese production of goods, but where did the need to calculate the volume come from? It is necessary to calculate the volume in order to find out overall volume cargo, and then choose the type of transport.
What is the calculation of volumes in delivery? And what role does he play?
Volume calculation- this is how, you already understood very much milestone in delivery, and you need to trust him in reliable hands professionals. The calculation of the volume of cargo must be done carefully, taking into account all dimensions, and converting them into cubic meters.
But unfortunately, not everyone copes with these calculations.
Also in school times we studied how to calculate the volume of cargo in m3, but unfortunately, you won’t remember all this. How to calculate the volume of cargo in m3 - there are times when this question comes to the fore, for example, during delivery.
For this this page and exists!
After all, that's what this page is for. to help you calculate shipping.
To calculate the volume of the box, you do not have to try to do it yourself, you just need to fill out empty fields. The calculation of the volume of the box will be automatically performed by our calculator, if in doubt, check for yourself.
To do this, we reminded you of the volume formula.
Calculation of cargo volume in cubic meters you need in order to submit the correct application for its carriage. Calculating the volume of cargo in cubic meters, i.e. knowing the volume itself will help you decide which type of delivery is right for you.
And now let's move on to the main, let's talk about how to make calculations and why they are needed.
To begin with, let's take a look…
Calculating the volume of cargo is not always easy, as it seems, all this is due to the fact that boxes can be of various shapes. Calculate cargo volume rectangular box, a trifle, but the rest is hard, you need to know the formulas.
To begin with, let's define the form, for this we first find out what they exist.
What shape can the box have?
- Rectangle;
- cylinder;
- Truncated pyramid (very rare).
Then comes the measurements
Before calculating the volume of the box, we will measure it, but remember, the more accurate the measurements are made, the easier it is for you. "How to calculate the volume of a box?" - what to do next: determine what shape it is (cube or rectangle), dimensions.
What does knowledge of volume give us?
Knowing the volume of the box will not allow misunderstandings when loading goods into any type of transport that may be. Almost nothing depends on the volume of the box, rather, on the contrary, everything depends on the size of the product itself.
And why? Everything is obvious here, before you buy a box, you need to find out the size of the cargo that you are going to transport across the border.
Well, now you know the dimensions of the cargo, now it remains to calculate its volume (in order to purchase a box).
So, in order to find out how to calculate the volume of cargo in m3, the formula will be required first. How to calculate the volume of cargo in m3, the formula will help without a doubt in this matter, this is how it looks like V = a * b * h, everything is very simple.
Especially since you already know it.
We would like to remind you that…
To make it easier for you to determine which type of transport to choose for delivery, you need to calculate the volume of cargo in m3. Calculating the volume of cargo in m3 is very simple, here you need to know exact dimensions, which then need to be multiplied.
Units must be converted exactly to m3, otherwise it will not be possible to calculate the delivery.
But what if the shape of the box is not rectangular, but rounded? After all, this is a rarity, but it still happens.
You can calculate the volume of boxes or containers at the base of which lies a circle, and there is also a formula for this. The expression V * r2 * h allows you to calculate the volume of the box in the shape of a circle, the dimensions must first be accurately measured.
Volume calculator
We bring to your attention a calculator: the volume of goods in m3, with the help of which you can independently make calculations. The cargo volume calculator is located on the rental website especially for your convenience and for quick calculations.
Why do you need a cargo volume calculator?
We are with you business people and Lost time sometimes comes with big downsides. Do you want to receive cargo quickly and reliably? And at the same time to the maximum short time find out the prices for their transportation and delivery?
This is where the cargo volume calculator will help!
Our volume calculator allows you to calculate the volume of cargo in m3, so the question of the volume of the box will no longer arise. The volume calculator is simple and easy to use, it will give the results of both the volume of the box and the load.
So, with the help of the volume calculator you solve several questions:
How to calculate the volume of cargo (or box)? Do not forget about the quantitative unit that you are taking into account.
Have you encountered one of them or have a similar one? Our company is pleased to offer for your convenience the volume in cubic meters of a box to calculate using a handy calculator.
And finally, let's remember the math!
What is the most common problem?
Many confuse how to calculate volume flat figures and voluminous, because they are mistaken in concepts, or rather find it difficult to answer. You don’t need to know how to calculate the volume, it’s enough that you indicate the dimensions, the main thing is not to forget that there are 3 of them.
Having finished all the calculations, there is one more task left.
What kind of transport do you need?
Recall that in delivery, in addition to how to calculate the cubic capacity, there are no less important things, for example, the placement of goods. You know how to calculate the cubic capacity, so everything else is in your hands, now the choice of transport is up to you.
Chemistry and physics always involve the calculation of various quantities, including the volume of a substance. The volume of a substance can be calculated using some formulas. The main thing is to know what condition it is in given substance. Aggregate states, in which particles can reside, there are four:
- gaseous;
- liquid;
- hard;
- plasma.
To calculate the volume of each of them has its own specific formula. In order to find the volume, you need to have certain data. These include mass, molar mass, and for (ideal) gases, the gas constant.
The process of finding the volume of a substance
Let's look at how to find the volume of a substance if it is, for example, in gaseous state. To calculate, you need to find out the conditions of the problem: what is known, what parameters are given. The formula for determining the volume of a given gas is:
Necessary molar amount of the available substance (referred to as n) times its molar volume (Vm). So you can find out the volume (V). When the gas is in normal conditions- n. y., then its Vm - volume in moles is 22.4 l. / mol. If the condition says how much substance there is in moles (n), then you need to substitute the data into the formula and find out final result.
If the conditions do not provide for the indication of data on the molar quantity (n), it must be found out. There is a formula to help you do the calculation:
Divide the mass of a substance (in grams) by its molar mass. Now you can do the calculation and determine the molar amount. M is a constant that can be viewed in the periodic table. Under each element there is a number that indicates its mass in moles.
Determining the volume of a substance in milliliters
How to determine the volume of a substance in milliliters? What can be indicated in the conditions of the problem: mass (in grams), consistency in moles, the amount of the substance given to you, as well as its density. There is such a formula by which you can calculate the volume:
The mass in grams must be divided by the density of the specified substance.
If you do not know the mass, then it can be calculated as follows:
The molar amount of a substance must be multiplied by its molar mass. In order to correctly calculate the molar mass (M), you need to know the formula of the substance that is given in the condition of the problem. Need to fold atomic mass each of the elements of matter. Also, if you need to know the density of a substance, you can use this inverse formula:
If you know the molar quantity (n) and concentration (c) of a substance, you can also calculate the volume. The formula will look like this:
You need to divide the molar amount of the given substance in the problem by its molar concentration. From this we can derive a formula for finding the concentration.
To correctly solve problems in physics and chemistry, you need to know some formulas and have the periodic table at hand, then success is guaranteed to you.
Any geometric body can be characterized by surface area (S) and volume (V). Area and volume are not the same thing. An object can have a relatively small V and a large S, for example, this is how the human brain works. It is much easier to calculate these indicators for simple geometric shapes.
Parallelepiped: definition, types and properties
The parallelepiped is quadrangular prism, at the base of which is a parallelogram. Why might you need a formula for finding the volume of a figure? Books, packing boxes and many other things from Everyday life. Rooms in residential and office buildings are usually cuboid. To install ventilation, air conditioning and determine the number of heating elements in a room, it is necessary to calculate the volume of the room.
The figure has 6 faces - parallelograms and 12 edges, two arbitrarily chosen faces are called bases. The parallelepiped can be of several types. The differences are due to the angles between adjacent edges. The formulas for finding the V-s of various polygons are slightly different.
If 6 faces geometric figure are rectangles, it is also called rectangular. The cube is special case a parallelepiped in which all 6 faces are equal squares. In this case, to find V, you need to know the length of only one side and raise it to the third power.
To solve problems, you will need knowledge not only of ready-made formulas, but of the properties of the figure. List of main properties rectangular prism small and very easy to understand:
- Opposite faces of the figure are equal and parallel. This means that the ribs located opposite are the same in length and angle of inclination.
- All side faces right parallelepiped- rectangles.
- The four main diagonals of a geometric figure intersect at one point, and divide it in half.
- Square diagonal of a parallelepiped equal to sum squares of measurements of the figure (follows from the Pythagorean theorem).
Pythagorean theorem states that the sum of the areas of the squares built on the legs of a right triangle is equal to the area of the triangle built on the hypotenuse of the same triangle.
The proof of the last property can be seen in the image below. The course of solving the problem is simple and does not require detailed explanations.
The formula for the volume of a rectangular parallelepiped
The formula for finding all types of geometric shapes is the same: V=S*h, where V is the desired volume, S is the area of the base of the parallelepiped, h is the height omitted from opposite peak and perpendicular to base. In a rectangle, h coincides with one of the sides of the figure, so to find the volume of a rectangular prism, you need to multiply three measurements.
The volume is usually expressed in cm3. Knowing all three values a, b and c, finding the volume of the figure is not at all difficult. The most common type of problem in the USE is the search for the volume or diagonal of a parallelepiped. Solve many typical tasks Unified State Examination without a formula for the volume of a rectangle is impossible. An example of a task and the design of its solution is shown in the figure below.
Note 1. The surface area of a rectangular prism can be found by multiplying by 2 the sum of the areas of the three faces of the figure: the base (ab) and two adjacent side faces (bc + ac).
Note 2. The surface area of the side faces can be easily found by multiplying the perimeter of the base by the height of the parallelepiped.
Based on the first property of parallelepipeds, AB = A1B1, and the face B1D1 = BD. According to the consequences of the Pythagorean theorem, the sum of all angles in right triangle is equal to 180 °, and the leg lying opposite the angle of 30 ° is equal to the hypotenuse. Applying this knowledge for a triangle, we can easily find the length of the sides AB and AD. Then we multiply the obtained values and calculate the volume of the parallelepiped.
The formula for finding the volume of a slanted box
To find the volume oblique parallelepiped it is necessary to multiply the area of \u200b\u200bthe base of the figure by the height lowered by given ground from the opposite corner.
Thus, the desired V can be represented as h - the number of sheets with an area S of the base, so the volume of the deck is made up of the Vs of all cards.
Examples of problem solving
Tasks single exam must be completed for certain time. Typical tasks usually do not contain a large number computing and complex fractions. Often a student is offered how to find the volume of an irregular geometric figure. In such cases, one should remember the simple rule that the total volume is equal to the sum V-s constituent parts.
As you can see from the example in the image above, there is nothing complicated in solving such problems. Tasks from more complex sections require knowledge of the Pythagorean theorem and its consequences, as well as the formula for the length of the diagonal of a figure. For successful solution test tasks, it is enough to familiarize yourself with samples of typical tasks in advance.
