Square Pyramid (cut)

Department Department

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EducationEducation

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Cut Square Pyramid - Problem

The given views show the Front Elevation and unfinished Plan of a cut square pyramid.

Draw the following views :-

The completed PlanEnd ElevationSurface Development of sidesTrue Shape of cut surface

Department of Technological EducationDepartment 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.

Department of Technological EducationDepartment of Technological Education

Number each of the points in each view.

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Finding Position of cut on End Elevation

Project from the Front Elevation to find the cut surface on the End Elevation.

Department of Technological EducationDepartment of Technological Education

Darken the outlines on the End Elevation.

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Finding Position of cut on Plan

Project from the Front Elevation to find the cut surface on the Plan.

Department of Technological EducationDepartment of Technological Education

Darken the outlines on the Plan.

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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

Department of Technological EducationDepartment of Technological Education

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.Project the point found onto the Elevation baseline and draw a generator to the apex of the pyramid.

Project the cut points from the elevation onto this True Length line.

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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.

Department of Technological EducationDepartment of Technological Education

Measure the length of the corner of the pyramid using the True Length line and draw a curve on the Development at this size.

Step off the length of each of the sides of the pyramid onto the Development.

Draw generators to each of these points to indicate the fold lines

Number each of the points.

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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.

Department of Technological EducationDepartment of Technological Education

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.

Darken the outlines on the Development.

Add the fold lines to complete the view.

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Alternative Layout

Drawing the True Shape

To find the True Shape, project the cut points away from the Front Elevation at right angles to the cut.

Department of Technological EducationDepartment of Technological Education

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.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.

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Drawing the True Shape

To find the True Shape, project the cut points away from the Front Elevation at right angles to the cut.

Department of Technological EducationDepartment of Technological Education

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.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.

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