THE planning of solids geometric is very useful for the calculation of the area and also for the creation of molds to assemble these solids. The main solids are the cube, the parallelepiped, the prism, the pyramid, the cylinder and the cone. There are different ways to plan a solid, which is the representation in two dimensions. To assemble a data, for example, we need to build the mold of that data, that is, its planning.
See too: Congruence of geometric figures – what are the criteria?
What is planning?
We know how to plan a geometric solid a representation of all your faces in two-dimensional shape, allowing you to visualize the whole of the solid. We also use the flat pattern as a template for creating these solids.
Cube Planning
The cube is one of the very common shapes in our daily lives. The die, for example, has the shape of a cube, as well as the magic cube and boxes. The cube is composed of 12 edges, 6 square faces and 8 vertices.
Cobblestone Planning
The parallelepiped can be identified in shoe boxes, bricks, among others. He has
6 faces (formed by quadrilaterals in the form of parallelograms), 12 edges and 8 vertices.
Read too: Sum of internal angles of a polygon
Planning prisms
Generally speaking, the prism is a polyhedron that have two equal bases, connected by the side faces. These bases can have various shapes, such as triangles, squares, pentagons, hexagons, among others. The number of faces, edges and vertices depends on the base. It is also very common in our daily lives, as there are boxes that have different shapes in their bases.
Pyramid Planning
At pyramids they can also have different bases, which can be triangular, square, pentagonal, among others. Planning also depends on the base of the pyramid., as well as the number of faces, vertices and edges. The pyramids in Egypt, for example, have a square base.
Cylinder Planning
The cylinder is a round body and is equally common in our daily lives. This is the geometric shape of soda cans, pipes, among other objects. The cylinder has two bases in the shape of a circle, and its side face is in the shape of a rectangle. In rounded solids, it doesn't make sense to talk about numbers of faces and edges, as they are rounded.
Also access: Convex Polygons and their Elements
Cone planning
O cone has a circular base, and its lateral area has the shape of an arc.. Objects such as an ice cream cone, a birthday hat, among others, are shaped like a cone.
solved exercises
Question 1 - (Enem 2012) Maria wants to innovate her packaging store and decided to sell boxes with different formats. In the images presented are the planning of these boxes.
What will be the geometric solids that Maria will obtain from the planning?
A) Cylinder, pentagonal base cousins and pyramid.
B) Cone, pentagonal base prism and pyramid.
C) Cone, trunk of pyramid and pyramid.
D) Cylinder, pyramid trunk and prism.
E) Cylinder, prism and cone frustum.
Resolution
Alternative A. Analyzing the characteristics of each of the flat patterns, we notice that the first one has two circular bases and a rectangular lateral area, so it is a cylinder. The second plane has two pentagonal bases, and the lateral areas are rectangular, which indicates that it is a prism with a pentagonal base.
Finally, the third figure has a triangular base in the middle, which makes it a pyramid with a triangular base.
Question 2 - (Enem 2015) A company that packs its products in cardboard boxes, in the form of a regular hexahedron, wants its logo printed on the opposite sides painted in gray, as shown in the figure:
The printer that will print the logos presented the following planned suggestions:
Which option suggested by the printer meets the company's desire?
THERE
B) II
C) III
D) IV
E) V
Resolution
Alternative C. Analyzing the plans, the alternative that has two opposite faces painted is III, which, when building the cube, respects the characteristics requested by the company. As for the others, when forming the box, the painted faces would be next to each other, contrary to the company's request.
