Goals
1. Understand the significance of developing three-dimensional figures.
2. Identify and analyze the construction of prisms, pyramids, cylinders, and cones.
3. Get acquainted with the vocabulary related to three-dimensional figures and their developments.
Contextualization
Three-dimensional figures are everywhere in our daily lives, from the homes we live in to the tools we use. Grasping how these figures can be represented on a two-dimensional plane is vital for various careers such as architecture, engineering, and design. For example, architects utilize these developments to create accurate building models, ensuring precision in measurements before breaking ground. Engineers apply this technique to design components that will come together to form larger structures, like bridges and vehicles. Product designers depend on developments to create packaging that is both functional and visually appealing.
Subject Relevance
To Remember!
Development of Prisms
The development of prisms includes sketching all faces of a prism on a two-dimensional surface so they can be cut and folded into the original three-dimensional figure. Each prism consists of two parallel and congruent polygons (the bases), along with lateral faces that are parallelograms.
-
Prisms have two parallel and congruent bases.
-
The lateral faces are parallelograms.
-
The development must include all the prism's faces.
-
Accuracy in measurements is crucial for accurately assembling the three-dimensional figure.
Development of Pyramids
The development of pyramids involves illustrating the base of the pyramid plus the triangular lateral faces on a two-dimensional plane. Each pyramid features a base that can be any polygon, while the lateral faces are always triangles.
-
Pyramids have a polygonal base with triangular lateral faces.
-
The development must include the base alongside all lateral faces.
-
Measuring accurately is vital for the lateral faces to align correctly with the base.
-
Each edge of the base needs to correspond with a lateral edge.
Development of Cylinders
The development of cylinders requires drawing two circles (the bases) and a rectangle that represents the cylinder's lateral surface. The rectangle should match the cylinder's height, while its length corresponds to the circumference of the bases.
-
Cylinders consist of two circular bases and a rectangular lateral surface.
-
The development must include two circles and one rectangle.
-
The height of the rectangle must equal the cylinder's height.
-
The rectangle's length must match the circumference of the bases.
Development of Cones
The development of cones involves drawing the circular base together with a circular sector that signifies the cone's lateral surface. The sector's radius must equal the cone's slant height, with an arc that matches the base's circumference.
-
Cones have a circular base and a lateral surface shaped like a circular sector.
-
The development must include the circular base and the circular sector.
-
The sector's radius must correspond to the cone's slant height.
-
The arc of the sector needs to align with the base's circumference.
Practical Applications
-
Architecture: Architects leverage developments to design and construct accurate building models before construction.
-
Engineering: Engineers implement developments to fabricate parts that will assemble into larger structures like bridges and vehicles.
-
Product Design: Product designers utilize development methods to craft packaging that is both practical and eye-catching.
Key Terms
-
Development: The representation of a three-dimensional figure on a two-dimensional surface.
-
Prism: A three-dimensional figure featuring two parallel and congruent bases alongside lateral faces that are parallelograms.
-
Pyramid: A three-dimensional figure with a polygonal base and triangular lateral faces.
-
Cylinder: A three-dimensional figure with two circular bases and a rectangular lateral surface.
-
Cone: A three-dimensional figure showcasing a circular base and a lateral surface that resembles a circular sector.
Questions for Reflections
-
In what ways can the ability to convert three-dimensional figures into flat drawings benefit various professions?
-
How might the development of three-dimensional figures help an architect or engineer in their daily tasks?
-
How can understanding developments lead to innovation in the job market?
Maker Challenge: Create Your Own Project
To reinforce your understanding of the development of three-dimensional figures, you will take on the challenge of creating your own project using the techniques we've learned.
Instructions
-
Select a three-dimensional figure you prefer (prism, pyramid, cylinder, or cone).
-
Draw the development of your chosen figure on cardboard, ensuring all measurements are precise.
-
Cut out and assemble the three-dimensional figure from the drawn development.
-
Feel free to personalize and decorate your figure, if you'd like.
-
Compose a short text explaining how the development aided in constructing the figure and discuss in which professions this skill may be applicable.
