Pyramid Construction Pyramids Square Rectangle Hex Cone

What are they ? See some examples How do you draw them ? Pyramid Construction What are they ? See some examples How do you draw them ?

Pyramid Construction What are they? They are 3-D shapes which start off with a simple shape such as a Square at the bottom ( THE BASE ) and rise up to a point. e.g. An Egyptian pyramid starts with a Square base

Pyramid Construction Some Examples Triangle Hexagon Circle Square

How do you draw them ? We will start with a Square Pyramid Pyramid Construction How do you draw them ? We will start with a Square Pyramid

The 2 drawings below both describe the Square prism shown in fig 1. Pyramid Construction The 2 drawings below both describe the Square prism shown in fig 1. Complete the elevation of each drawing. Complete the end elevation of each drawing

Complete the elevation of the drawing. Pyramid Construction Complete the elevation of the drawing. Complete the end elevation of the drawing Produce the surface development

Complete the elevation of each drawing. Pyramid Construction Complete the elevation of each drawing. Complete the end elevation of each drawing Produce the development

Pyramid Construction 1 2 4 3 1/4 2/3

Pyramid Construction 1 2 4 3 1 /4 2 /3 3 /4 1 /2

Pyramid Construction 1 2 4 3 1 /4 2 /3 3 /4 1 /2

Pyramid Construction

Pyramid Construction 1 2 4 3 1 /4 2 /3 3 /4 1 /2

Pyramid Construction 1 2 4 3 1 /4 2 /3 3 /4 1 /2 1

Pyramid Construction 1 1 2 4 4 3 3 2 1 /4 2 /3 3 /4 1 /2 1

Pyramid Construction Outline to Finish 1 1 2 4 4 3 3 2 1 /4 2 /3 3 /4 1 /2 1

Pyramid Construction

4 3 1 2 Front Elevation End Elevation (4) 1 (3) 2 (1) 2 (4) 3 Pyramid Construction 4 3 1 2 Front Elevation End Elevation (4) 1 (3) 2 (1) 2 (4) 3

Development of a Rectangular Pyramid Pyramid Construction Development of a Rectangular Pyramid How many sides does it have? 5 4 Triangles and 1 Rectangle Describe the shapes of the sides Are all the triangles the same? No Why? Because two edges on the base are long and two are short. This creates two different sizes of triangle.

Pyramid Construction The Development Base

Preferred Method Why? Imagine this shape being made from sheet metal. Pyramid Construction Preferred Method Why? Imagine this shape being made from sheet metal. Base Less cutting Less waste Less joining

Drawing Method Step 1 - Draw the base Pyramid Construction Drawing Method Step 1 - Draw the base Step 2 requires a True Length which isn’t on the drawing and has to be created

Construct the True Length Pyramid Construction Step 3 Construct the True Length Front Elevation Because your eye is at right angles to the red line in the plan, the red line in the Front Elevation is a true length True length

Using the True Length Step 4 Pyramid Construction Using the True Length True length Step 4 Use the true length to construct the four sides

Pyramid Construction

Solid Hexagonal Pyramid Multi-View Pyramid Construction Solid Hexagonal Pyramid Multi-View

Pyramid Construction Drawing the Plan View 1 2 6 3 5 4 3/2 4/1 5/6

Drawing the End Elevation View Pyramid Construction Drawing the End Elevation View 1 2 6 3 5 4 3/2 4/1 5/6 4 5/3 6/2 1

Drawing the Surface Development Pyramid Construction Drawing the Surface Development Use a compass and lift the true length of the pyramid edge. Draw a horizontal and vertical centre line to indicate the apex of the surface development Draw a large Arc with the compass set to the true length. Draw a line between the apex and the arc. This is the first edge Use a compass and lift the length of side from the plan Transfer this size to successive points on the arc. At each mark draw a line across. Draw a straight line between the arc points. Now draw, using a 30o/600 set square, one hexagon in the positions shown.

Pyramid Construction Outline to Finish 6 1 2 3 4 5 5/6 4/1 3/2 5/3 6/2

Pyramid Construction

Cut Square Pyramid - Question Pyramid Construction Department of Technological Education Cut Square Pyramid - Question The given views show the Front Elevation and unfinished Plan of a cut square pyramid. Draw the following views :- The completed Plan End Elevation Surface Development of sides True Shape of cut

Finding Position of End Elevation Pyramid Construction Department of Technological Education Finding Position of End Elevation Using the Plan and the Front Elevation project the position of the End Elevation and show the slope of the sides. 1 2 Number each of the points in each view. 4 3 1 /4 2 /3 3 /4 1 /2

Finding Position of cut on End Elevation Pyramid Construction Department of Technological Education Department of Technological Education Finding Position of cut on End Elevation Project from the Front Elevation to find the cut surface on the End Elevation. 1 2 Darken the outlines on the End Elevation. 4 3 1 /4 2 /3 3 /4 1 /2

Finding Position of cut on Plan Pyramid Construction Department of Technological Education Finding Position of cut on Plan Project from the Front Elevation to find the cut surface on the Plan. 1 2 Darken the outlines on the Plan. 4 3 3 /2 1 /4 1 /4 2 /3

Finding True Length of pyramid corner Pyramid Construction Department of Technological Education Finding True Length of pyramid corner Before the Development can be drawn it is necessary to find out the True Length of the corner of the pyramid so that accurate sizes for the development and the cut points can be found 1 2 3 /3 /2 1 /4 Draw a curve on the plan with the centre being located at the centre of the pyramid, the radius being measured at one of the corners, and the end point of the curve being the centre line. 4 Project the point found onto the Elevation baseline and draw a generator to the apex of the pyramid. 1 /4 Project the cut points from the elevation onto this True Length line.

Drawing the outline of the Development Pyramid Construction Department of Technological Education Drawing the outline of the Development Indicate where the development is going to be placed, and then draw the first generator to indicate one corner of the pyramid. 1 2 1 3 4 Measure the length of the corner of the pyramid using the True Length line and draw a curve on the Development at this size. 2 Step off the length of each of the sides of the pyramid onto the Development. 3 Draw generators to each of these points to indicate the fold lines Number each of the points. 1 /4 2 /3 3 /4 1 /2 4 1

Drawing the cut on the Development Pyramid Construction Department of Technological Education Drawing the cut on the Development Step off from the True Length line the distance from the apex of the pyramid to each cut point and transfer these sizes to the correct generators on the Development. 1 4 /4 2 3 /3 /2 1 /4 1 2 Join each of the points to show the developed shape of the cut. Also add the flat edges to the base of the pyramid on the Development. 3 Darken the outlines on the Development. Add the fold lines to complete the view. 4 1

Drawing the True Shape Department of Technological Education Pyramid Construction Department of Technological Education Drawing the True Shape To find the True Shape, project the cut points away from the Front Elevation at right angles to the cut. 1 2 1 2 3 4 Draw a datum line on the True Shape parallel to the cut line of the Front Elevation and at right angles to the lines just projected. Use the centre line of the plan as a datum line. 4 3 1 /4 2 /3 3 /2 Measure the vertical distances from the datum to each of the cut points on the plan. Transfer each of these sizes on to the True Shape. Join each of the points found to produce the True Shape. Complete the view by darkening the outlines.

Pyramid Construction Department of Technological Education Cut cone The given views show the Front Elevation and part Plan of a cut cone. Draw the following views :- Complete Plan End Elevation Development True Shape of cut

Finding position of End Elevation Pyramid Construction Department of Technological Education Finding position of End Elevation Start drawing the End Elevation by projecting the height and width from the given views.

Drawing Generators on Plan Pyramid Construction Department of Technological Education Drawing Generators on Plan Use 30o and 60o lines to divide the Plan into 12 equal parts. 11 12 1 10 2 Number each of the points on the Plan. 9 3 8 4 7 5 6

Transfer Generators from Plan to Elevation Pyramid Construction Department of Technological Education Transfer Generators from Plan to Elevation Project each of the points from the Plan onto the Elevation base. 11 12 1 10 2 9 Number each of the points on the Elevation making sure that the numbers correspond with those on the Plan. 3 8 4 7 5 6 10 11 12 1 2 9 3 8 7 6 5 4

Drawing generator on Elevation Pyramid Construction Department of Technological Education Drawing generator on Elevation Draw generators from the apex of the cone to each of the points found on the base of the cone. 1 2 9 8 7 6 5 4 3 1 2 3 4 5 6 7 8 9 10 11 12

Drawing generators onto End Elevation Pyramid Construction Department of Technological Education Drawing generators onto End Elevation Project the position of the generators onto the End Elevation by projecting the points from the Plan. 12 11 10 9 8 7 6 5 4 3 2 1 1 Number each of the points on the End Elevation. Draw generators from the apex to the base. 9 1 8 7 2 6 5 4 3 7 8 9 10 11 6 12 5 4 3 2 1

Finding cut points on End Elevation Pyramid Construction Department of Technological Education Finding cut points on End Elevation Project the points where the generators on the Elevation cross the cut onto the End Elevation. 12 11 10 9 8 7 6 5 4 3 2 1 Mark each of the points found with a small dot. 9 1 8 7 2 6 5 4 3 6 5 8 4 3 10 2 11 1 12 7 9

Completing End Elevation Pyramid Construction Department of Technological Education Completing End Elevation Complete the End Elevation by drawing a smooth curve through each of the point and then darkening the other outlines on the view. 1 2 1 1 1 1 2 9 3 8 4 7 5 6 9 1 8 7 2 6 5 4 3 6 5 8 4 3 10 2 11 1 12 7 9

Finding cut points on Plan Pyramid Construction Department of Technological Education Finding cut points on Plan Project the points from the cut on the Elevation up to the correct generator lines on the Plan. (Note that points 6 and 12 will not be able to be found at this time.) 1 2 1 1 1 1 2 9 3 8 4 7 5 6 9 1 8 7 2 6 5 4 3 Mark each of the points found with a small dot 6 5 8 4 3 10 2 11 1 12 7 9

Finding points 6 and 12 on Plan (alternative 1) Pyramid Construction Department of Technological Education Finding points 6 and 12 on Plan (alternative 1) Project point 6 and 12 onto the outside generator on the Elevation. 1 2 1 1 1 1 9 8 2 Project this point up to the centre line of the Plan. 3 4 7 5 6 Use compasses to rotate this point onto the correct generators for points 6 and 12. Mark each of these points with a small dot 9 1 8 7 2 6 1 2 7 3 8 9 1 1 1 6 5 1 2 5 4 4 3 2 1

Finding points 6 and 12 on Plan (alternative 2) Pyramid Construction Department of Technological Education Finding points 6 and 12 on Plan (alternative 2) Project points 6 and 12 from the End Elevation onto the correct generators on the Plan. 1 2 1 9 8 1 2 3 7 6 5 4 8 4 3 2 1 9 1 1 1 1 2 1 2 7 3 8 9 1 1 1 6 5 1 2

Pyramid Construction Department of Technological Education Completing Plan To complete the Plan draw a smooth curve through each of the 12 points found. 1 2 1 1 1 1 2 9 3 8 4 7 5 6 9 1 1 1 1 2 1 2 7 3 8 9 1 1 1 6 8 7 6 5 4 5 1 2 4 3 2 1

Development of surface (1) Pyramid Construction Department of Technological Education Department of Technological Education Development of surface (1) Mark the position where the apex of the Development will be placed. 1 2 9 8 7 6 5 4 3 9 Draw the first generator. 10 11 Draw the base line of the Development. 12 Step off the size to each generator point along the base. 1 2 Number each of the points found. 3 Draw generator lines from the apex to each of the points on the base. 4 5 6 7 9 8

Development of surface (2) Pyramid Construction Department of Technological Education Development of surface (2) It is necessary to find the ‘true length’ of the cut points along each generator. To find these sizes project a line through each point on the cut of the Elevation to the outside generator. 1 2 9 8 7 6 5 4 3 6 7 5 8 4 9 3 1 2 9 1 8 7 2 6 Mark each of the found points with a small dot. 1 2 3 5 4

Development of surface (3) Pyramid Construction Department of Technological Education Development of surface (3) Measure the distance from the apex to each point on the outside generator. 1 2 1 1 1 1 9 2 Transfer this size to the correct generator on the Development. 1 9 3 1 1 8 4 1 2 Mark each point with a small dot. 7 5 6 1 Draw a smooth curve through each point found. 2 3 4 Darken each of the other outlines on the Development. 5 6 7 9 1 1 1 1 2 1 2 7 3 8 9 1 1 1 8 6 5 1 2 9 8 7 6 5 4 4 3 2 1

Pyramid Construction Department of Technological Education True Shape of cut (1) Project each of the points on the cut of the Elevation away at right angles to the cut surface. 9 10 8 11 1 2 9 8 7 6 5 4 3 7 12 6 1 5 9 1 2 4 3 Draw a datum line on the True Shape – in this case the centre line has been chosen. 1 2 8 7 6 5 4 3 9 Number each of the lines projected up to the True Shape.

Pyramid Construction Department of Technological Education True Shape of cut (2) Measure the sizes from the cut points to the centre line on the Plan and transfer each of these sizes to the correct lines on the True Shape. Note – These sizes can also be measured from the End Elevation. Mark each of the points with a small dot. 9 10 8 11 1 2 9 8 7 6 5 4 3 7 12 6 1 5 9 2 4 1 3 1 1 1 2 1 2 3 4 5 6 7 9 8

Pyramid Construction Department of Technological Education True Shape of cut (3) To finish the True Shape draw a smooth curve through each of the points found. 1 2 9 8 7 6 5 4 3 11 12 10 The final drawing should look like this.

Pyramid Construction

Pyramid Construction SUMMARY

Pyramid Construction

Pyramid Construction