27. Areas and volumes of geometric figures

Página 27

The areas and volumes of geometric figures are fundamental concepts in mathematics, being widely covered in exams such as the ENEM. The study of these measurements is essential for solving geometry problems, where it is necessary to calculate the extension of a surface or the capacity of a solid.

To start off, let's talk about the area. The area is the measure of the extent of a surface. It is calculated in units of measurement squared (such as square meters, square centimeters, etc.). Each geometric figure has a specific formula for calculating the area. For example, the area of ​​a rectangle is given by the product of the base and the height, while the area of ​​a circle is given by the formula πr², where r is the radius of the circle.

Next, let's talk about volume. Volume is a measure of the capacity of a solid. It is calculated in cubed units of measure (such as cubic meters, cubic centimeters, etc.). Like the area, each geometric solid has a specific formula for calculating the volume. For example, the volume of a cube is given by the cube of the edge, while the volume of a sphere is given by the formula 4/3πr³, where r is the radius of the sphere.

Now that we know what area and volume are, let's learn how to calculate these measurements for some of the main figures and geometric solids.

Area of ​​rectangle

The area of ​​the rectangle is given by the product of the base by the height. If the base of the rectangle measures b and the height measures h, the area A is given by the formula A = b*h.

Area of ​​circle

The area of ​​the circle is given by the formula A = πr², where r is the radius of the circle. The number π (pi) is a mathematical constant whose approximate value is 3.14.

Volume of cube

The volume of the cube is given by the cube of the edge. If the edge of the cube measures a, the volume V is given by the formula V = a³.

Sphere volume

The volume of the sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. Again, the number π (pi) is a mathematical constant whose approximate value is 3.14.

It is important to remember that, in order to calculate the area and volume of figures and geometric solids, it is necessary to know the measurements of their dimensions (such as the base, height, radius, edge, etc.). Furthermore, one must bear in mind that the formulas presented here are valid only for the figures and solids mentioned. Other figures and solids have different formulas, which must be studied separately.

In summary, the study of areas and volumes of geometric figures is fundamental for solving geometry problems. In addition, these concepts are widely covered in exams such as the ENEM, and mastering the formulas and knowing how to apply them correctly is essential for student success.

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2828. Ratios and proportions