In solving a number of problems in mathematics and physics, as well as in carrying out agronomic work on sown areas, knowledge and ability to calculate the surface area of the earth and other objects are required. This article is devoted to the question of how many square meters.
What is surface area?
This term refers to a certain quantity, which is characterized by two spatial one-dimensional parameters: length and width. The area in the SI system is measured in square meters.
To calculate the area the main role is played by the shape of the body under consideration. For example, if we are talking about a square, then its area can be calculated by the formula S = a 2 , where a is the parameter of its side (that is, the width is equal to the length), but if you are considering a circle, then to get this value, you need already a square multiply the radius by the number Pi, that is, S = pi * r 2 .
What is weaving?
To understand how many meters in a hundredth, you should give her a definition. Weaving is an off-system unit for measuring area, which is quite convenient for solving problems in agronomy. It corresponds to 100 square meters.
How can you imagine this area? Very simple. It is necessary to draw a square on the surface of the earth, the side of which will be 10 meters. Indeed, since the area of the square is equal to the product of its sides, we obtain 10 * 10 = 100 m 2 , which corresponds to the area of one hundredth. This unit can be considered the smallest when measuring land.
In addition to weaving, land areas are often measured in hectares (Ha). This unit of measure is equal to one hundred hundredths, that is, 100 * 100 = 10,000 m 2 . Accordingly, one hectare covers an area equal to a square with a side of 100 meters.
It is interesting to note that for the first time the need for calculating land areas arose in ancient Egypt. This was due to the fact that the Nile River overflowed the banks every year, so the Egyptians needed to know what area it was flooding in order to plan its agricultural activities. According to the Greek historian Herodotus, this fact prompted the inhabitants of the country of the pharaohs to introduce not only the unit of measurement of the area, but also to invent the geometry itself.
Examples of solving problems
Knowing how many square meters are, we will solve two simple problems:
- Task 1. It is known that a tractor can plow 2500 acres of land every day. It is necessary to calculate how many days it will take for him to plow the entire field, which is 2 km long and 1.5 km wide. To solve this problem, it is necessary to convert all quantities into the same unit of measurement. We will use square meters. So, 2500 acres is 2500 * 100 = 250 000 m 2 . The area of the field is 2000 * 1500 = 3,000,000 m 2 . Dividing the second value by the first, we get: 3,000,000 / 250,000 = 12, that is, the tractor will need 12 days to plow the entire field.
- Task 2. It is necessary to determine the radius of a circle whose area is equal to one hundredth. To solve the problem, we use the formula for the area of the indicated flat figure. Expressing the radius, we get: r = √ (S / pi). Knowing the value of the number pi, and how many meters in a hundredth, we substitute the corresponding numbers, we get: r = √ (100 / 3.1416) = 5.64 meters. If the center of this circle is combined with a square of one hundred square meters, the circle will go beyond it, crossing each of the 4 sides, while the calculated radius is less than half the diagonal of the corresponding square (it is 7.07 meters).