The image on the right shows an abstract metal sculpture which is made from several intersecting solids - Leaving Cert DCG - Question B-2 - 2012
Question B-2
The image on the right shows an abstract metal sculpture which is made from several intersecting solids.
Fig. B-2 below shows the incomplete projections of two soli... show full transcript
Worked Solution & Example Answer:The image on the right shows an abstract metal sculpture which is made from several intersecting solids - Leaving Cert DCG - Question B-2 - 2012
Step 1
Draw elevation of given pyramid
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Answer
To draw the elevation of the triangular-based pyramid, start by identifying the dimensions provided. The triangular base is inclined at 30°, with the height of the pyramid equal to 30mm. Sketch the outline of the triangular elevation. Ensure that the apex is positioned vertically above the center of the triangle to respect the elevation views.
Step 2
Draw plan of pyramid
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Answer
The plan view of the pyramid can be drawn by projecting the point of the apex vertically down to the base. The base angles formed by the slants must be reflected accurately from the elevation. Ensure the dimensions match up, particularly that the base measures 60mm on each side.
Step 3
Position and draw cross-section view
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Answer
First, locate the position of the triangular prism at the intersection with the pyramid in both the elevation and plan views. The triangular prism should have a base of 65mm. Draw the cross-section view as it would appear intersecting the pyramid, taking care to clearly represent the dimensions and angles.
Step 4
Draw outline elevation of inclined prism
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Answer
Draw the outline elevation of the triangular prism, ensuring the triangular base is accurately represented. The outline should clearly show the two edges meeting the pyramid at the appropriate angles.
Step 5
Draw outline plan of prism, incl. triangular end
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Answer
For the plan view of the prism, draw the triangular outline at the corresponding angle to match that of the elevation. Include the triangular end of the prism, ensuring the dimensions are correctly represented, with the base of 65mm consistent with previous drawings.
Step 6
Determine points a, b & c in elevation and plan
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Identify points a, b, and c where the prism intersects the pyramid. Mark these points clearly in both the elevation and plan views.
Step 7
Draw “intersection triangle”
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Answer
Construct the intersection triangle by connecting the points a, b, and c. This triangle should be encapsulated within the pyramid's base, showcasing the intersection clearly.
Step 8
Determine points d, e & f in elevation and plan
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Next, locate points d and e, which will correspond to the edges of the triangular prism as seen in the elevation and plan views. Ensure these points relate directly to the intersection with the pyramid.
Step 9
Draw d & f in elevation and plan
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Incorporate the points d and f into both the elevation and plan drawings by projecting these points based on the previously defined geometry. Ensure their positions respect the intersecting prism.
Step 10
Joining up of lines in correct order
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Connect all relevant lines from the points indicated. Each line must correspond with the geometrical structure, showing the boundaries between the penetrating solids.
Step 11
Hidden detail
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Identify and sketch the hidden details for areas of the structure not directly visible. Use dashed lines to represent these features, ensuring clarity in the overall drawing.
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