Lesson Notes By Weeks and Term v4 - JHS 3
COMMUNICATING DESIGNS
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COMMUNICATING DESIGNS
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Subject: Career Technology
Class: JHS 3
Term: 2nd Term
Week: 12
Grade code: B9.5.1.1.2
Strand code: 5
Sub-strand code: 1
Content standard code: B9.3.3.1
Indicator code: B9.5.1.1.2
Theme: DESIGNING AND MAKING OF ARTEFACTS/PRODUCTS
Subtheme: COMMUNICATING DESIGNS
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This lesson introduces the concept of surface development, focusing specifically on pyramids. Surface development is a crucial skill in technical drawing and manufacturing. It involves creating a 2D flat pattern (called a 'net') that can be cut and folded to form a 3D object. In Ghana, this skill is vital for industries like packaging (e.g., creating boxes for shea butter or cocoa powder), sheet metal work (e.g., making funnels or roofing components), and even in craft making. By learning this, learners will be able to translate a 3D design idea into a practical 2D pattern for construction.
A. What is a Pyramid? A pyramid is a 3-dimensional solid object with a flat polygon base and triangular faces that meet at a common point called the apex. Base: The flat bottom face of the pyramid (e.g., a square, triangle, hexagon). Apex: The single point or vertex at the top where all the triangular faces meet. Slant Edge: The edge connecting the apex to a vertex of the base. Slant Height: The height of one of the triangular faces, measured from the midpoint of a base edge to the apex. True Height (Altitude): The perpendicular distance from the apex to the center of the base. B. What is Surface Development? Surface development is the process of "unrolling" or "unfolding" a 3D object to lay it flat. The resulting 2D shape is called a net. This net shows the true size and shape of all the surfaces of the object. When this net is cut out and folded along the edges, it will form the original 3D object. C. The Importance of "True Length" In orthographic projection (plan and elevation drawings), a line only shows its true length if it is parallel to the plane of projection. When we look at the front elevation of a pyramid, the slant edges appear shorter than they actually are, unless one of them is perfectly parallel to our line of sight. To create an accurate development, we MUST find the true length of the slant edges.
Method to Find True Length (Revolution Method): Draw the plan and front elevation of the pyramid. In the plan view, choose one slant edge (e.g., O-A). With the center of the base (O) as the pivot, use a compass to rotate this line until it is horizontal. Let's call the new point A'. Project this new point A' vertically upwards to the base line (XY line) in the front elevation. Draw a line from the apex in the front elevation to this new point on the base line. This new line is the True Length (TL) of the slant edge. All slant edges of a right regular pyramid are equal, so we only need to find the true length of one. D. Method of Development: Radial Line Method Because all the triangular faces of a pyramid meet at the apex, we can develop the surface by using one of the slant edges as a radius. Find the true length of the slant edge. Pick a point on your drawing sheet to be the apex (O) of the development. Set your compass to the True Length. With O as the center, draw a large arc. Step off the length of each side of the base along this arc. For example, for a square base of side 40mm, you will mark off 40mm sections on the arc. Connect these points on the arc to each other with straight lines, and connect them back to the apex (O). Finally, draw the base attached to one of the triangular faces.
Guided Practice (With Solutions) Question 1: Develop the surface of a square-based pyramid. A square pyramid has a base side of 40mm and a true height of 50mm. Draw the plan, front elevation, and the full surface development.
Solution: