To calculate the volume of a cube or cuboid you need to know three values: length, width and height. To calculate the mass required volume and density of the material of the object (m = v*ρ). The density of gases, liquids, rocks, etc. can be found in the relevant tables.
Example 1. Find the mass of a granite block, whose length is 7 m, width and height 3 m. the Volume of such a parallelepiped will be equal to V = l*d*h, V = 7m*3M*3M = 63 m3. The density of granite is 2.6 t/m3. The mass of the granite block: 2.6 t/m3 * 63 m3 = 163,8 T. a: 163,8 tonnes.
You need to consider that the sample may not be uniform or may contain impurities. In this case, you will need not only the density of the base material, but the density of impurities.
Example 2. Find the mass of a cube with sides 6 cm, which consists of 70% pine and 30% spruce. The volume of a cube with a side l = 6 cm is 216 cm3 (V=l*l*l). The volume that is occupied in the specimen pine, can be calculated using a proportion:216 cm3 - 100% X – 70%; X = 151,2 cm3
The volume that is occupied by spruce: 216 cm3 - cm3 151,2 = 64,8 cm3. Pine density of 0.52 g/cm3, so the mass of pines, contained in the sample of 0.52 g/cm3*cm3 151,2 = 78,624 g ate Density of 0.45 g/cm3, respectively - the mass is equal to 0.45 g/cm3*64,8 cm3 = amounted to 29.16 g. Answer: the total mass of the sample, consisting of spruce and pine 78,624 g + amounted to 29.16 g = 107,784 g
And even if you need to calculate the mass of a square sheet metal, then you will calculate the mass of the parallelepiped whose length l, width d and height (sheet thickness) h.
Example 3. Find the mass of copper square sheet, 10 cm by 10 cm, thickness 0,02 see the Density of copper 89,6 g/cm3. The volume of copper sheet: 10 cm*10 cm*0.02 cm = 2 cm3. m(sheet) = 2 cm3*89,6 g/cm3 = 179,2 g Answer: the mass of the sheet - 179,2 g.
In metal, there is the concept of mass of a square. This refers to the mass of calibrated metal rod with a square cross-section. But, regardless of how "this" is, in fact, this rod is still the same box.
Advice 2: How to find proportion
In mathematics, a ratio is called the equality of two relations. For all its parts characteristic of the interdependence and constant result. It is sufficient to consider one example to understand the principle of solving proportions.
Inspect the properties of proportions. The numbers on the edges of the equality is called extreme, and in the middle – average. The main property of proportions is that the middle and the extreme side of the equation can be multiplied among themselves. Enough to take the proportion 8:4=6:3. If you multiply the extreme parts together, you get 8*3=24 and the multiplication of the averages. This means that the product of the extreme parts of the ratio is always equal to the product of its average parts.
Take advantage of the fundamental property of proportions to calculate the unknown member in the equation for x:4=8:2. For finding the unknown parts of a proportion you must use the rule of equivalence of average and extreme parts. Write the equation in the form x*2=4*8, that is x*2=32. Solve this equation (32/2), you will receive the missing member of the proportion (16).
Simplify the ratio if it consists of fractional or large numbers. To do this, divide or multiply both members on the same number. For example, the component parts of a 80:20 proportion=120:30 can be simplified, dividing its members into 10 (8:2=12:3). You will get an equivalent equality. The same thing happens if you increase all members of the proportion, for example, 2, thus 160:40=240:60.
Try to move your parts of proportions. For example, 6:10=24:40. Swap the extreme end (40:10=24:6), or at the same time rearrange all the parts (40:24=10:6). All received proportions are equal. So you can get some equations from one.
Solve the proportion with interest. Make a note of it, for example, in the form: 25=100%, 5=x. Now we need to multiply the average members (5*100) and divide by the known extreme (25). In the end, it turns out that x=20%. Similarly, you can multiply the known extreme members and to divide them into existing medium, receiving the desired result.