Irregular cube volume calculation, the volume of an irregular object

To calculate the volume of an irregular three-dimensional figure, you can put this object in water, using the current volume - the volume of the unplaced object is the volume or the height after putting the object - the length * width of the object (1 liter = 1 cubic decimeter; 1 ml = 1 cubic centimeter).

The SI system of units for volume is cubic meters. The volume of a solid object is a numerical value used to describe the space occupied by the object in three-dimensional space. One-dimensional objects (e.g., lines) and two-dimensional objects (e.g., squares) are zero-volume in three-dimensional space.

1. Sphere: Sphere volume = 4 3 (pi to the third power of the radius) <>

2. Prism: v: volume; s1: upper surface area; s2: lower surface area; H: High.

3. Physical formula: volume = mass divided by density.

The volume of the bevel = the sum of the upper and lower base areas of the bevel plus the sum of the arithmetic square roots of the product of the area of the lower base and the product of the height of 1 3. This is v=(1 3)[s1+ (s1s2)+s2] h ( for square root).

The area of the upper base plus the area of the bottom base is multiplied by the height divided by 2

The volume of an irregular object is related to the height of the container (bottom area or length or width) and water (rising or falling). Volume of the irregular object = (bottom area of the container height of rising or falling water). Board Book:

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Scheme 1: Fill the container with enough liquid (usually water), then write down the volume of the liquid in the container as v1, then put the irregular object into the container, measure the total volume of the liquid and the irregular object as v2, and finally subtract v1 with v2 to get the volume of the irregular object.

Option 2: If you already know the density of an irregular object, you can first measure the mass of the object with a balance, and then use the density formula to calculate the volume of the irregular object.

Scheme 3: The measurement tool key is a balance, and the density is also unknown. First, fill the container with water, then place the irregular object in the water sublight, and then measure the volume of the overflowing water, which is equivalent to the volume of the irregular object.

The mass of the irregular object is then measured, and finally the volume is calculated using the density formula.

In fact, the calculation of the volume of irregular objects is relatively simple, so don't think too complicated about the problem.

To find the volume of an irregular object, there are formulas for the water position exchange method, a formula for the plane section method, and a formula for using regular objects by the segmentation method.

1. Water position change method.

The formula is: the volume of the irregular object = the difference in the total water volume before and after the submerged object. This method requires a container that is large enough, fills it with water, and records the height of the water level.

Then the irregular object to be measured is completely immersed in water to observe the change of water level, and the water level height at this time is recorded, and the total water volume after submerging the object is the existing water volume minus the previous water volume, and the object volume can be obtained.

2. Plane section method.

The formula is: volume of irregular object = (cross-sectional area of each layer and layer spacing). This method requires cutting an irregular object into many parallel sections at a certain interval, usually choosing a location with fewer cross-sections or a regular pattern for measurement.

Use a ruler or measuring instrument to measure the area and layer spacing of each section, multiply them, and add up the volume values of all sections to get the total volume.

3. Segmentation method.

The formula is the volume formula of the object with the help of other rules. This method is to divide the irregular object into several simple geometric bodies, such as Yanna cuboids, cylinders, cones, platforms, etc., and then calculate their volumes separately, and then sum them to obtain the total volume of the irregular objects.

For example, if an irregular object can be divided into a cuboid and a hemisphere, then its total volume is v=abc+2 3 r3 where. abc is the length, width, and height of the cuboid, and r is the radius of the hemisphere.

Precautions for finding irregular volumes:

1. Accurately measure the size.

To accurately calculate the volume of an irregular object, first of all, the size of the object needs to be measured. It is usually possible to measure using a measuring tool such as a tape measure and then calculate it according to a formula. When making measurements, you need to pay attention to the accuracy of the measurement to avoid errors in the results.

2. Deal with the density problem.

Solving the volume of an irregular object requires knowing its density because there is a definite relationship between volume and density. If the density of the object is not provided, the final calculation will also be affected. In this case, the corresponding density value can be obtained by referring to authoritative materials or conducting experimental measurements.

3. The problem of result trade-off.

When calculating the volume of irregular objects, it is often difficult to obtain completely accurate results due to various factors such as measurement accuracy and calculation error. Therefore, it is necessary to consider this situation when choosing the final result, and make reasonable decisions based on the actual needs and characteristics of the problem.

1. The easiest and easiest way to calculate the volume of irregular shapes with a measuring cup is to use a measuring cup, as long as you put a certain amount of water in the measuring cup to look at the scale, throw it into an object with irregular shape, and then look at the scale, the difference between the two quantities is the volume of the irregular shape. (Turning an irregular shape into a regular shape.) 2. The calculation principle of the container containing water is the difference between the total volume after submerging the object and the volume before submerging, and the volume of the irregular object submerged into the container containing water is obtained by subtracting the volume before submerging the volume before submerging.

The volume of water discharged is the volume of an irregular object. Fill the container with water, then slowly put the irregular object into the container, put a measuring cup at the mouth of the container, and the volume of water flowing out is the volume of the irregular object. 3. Use special objects to calculate the volume of irregular objects, for example, a large ball and a small ball discharge 12ml of water, and put in 3 small balls, and the water is discharged to 24ml, which means that the volume of 3 small balls and 12ml, then the volume of each small ball is the quotient of 12 and 3, that is, 4ml, then the volume of the big ball is the difference between 12ml and 4, that is, 8ml.

In a specific problem, the volume of an irregular object can be found based on the corresponding data. 4. If you use soil clods to calculate some objects that are not convenient to put into water, you can't use the above methods, such as soil clods, such as water-absorbing substances, then you can replace water with soil or sand to measure, and the calculation method is the same as that of water. 5. Divide the irregular polygon into several regular volumes.

, divide into several regular volumes, sum them, or add several regular regular volumes to form a regular volume, and then subtract the supplementary volume.

1.Prepare a cylindrical container, measure the diameter from the inner wall, pour in enough water, and measure the height of the outlet.

2.Measure the height of the water by placing an irregular object in the water.

3.The height of the water in the first measurement minus the height of the water in the second measurement multiplied by the base area of the cylinder (i.e., 2 r squared) is the volume of this irregular object.

Divide the pieces into regular calculated volumes and add them up.

A regular object can be found by integral.

I believe that many friends don't know how to calculate the volume of irregular objects, in fact, we can use a variety of methods to calculate, come and take a look with me.

01 If it is not feasible to multiply the length by the width by the height, we have to consider this problem from the perspective of physical brightness.

02 You can find a container with water, and it is best to find the kind with a unit, fill a part of the water, and then put the irregular object in it, 03 The number of the water level ** is the volume of the object, of course, we can also use this flexibly, such as the method shown in the figure below.

04 We can also measure the increase in the water level when an irregular object is placed in a container without a unit, and then find it by finding the volume formula for water.