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The 3D graphic below shows a display box, for chocolate eggs, which is based on a truncated prism - Leaving Cert DCG - Question A-1 - 2015
Question A-1
The 3D graphic below shows a display box, for chocolate eggs, which is based on a truncated prism. The drawing below shows the incomplete pictorial and orthographic ... show full transcript
Worked Solution & Example Answer:The 3D graphic below shows a display box, for chocolate eggs, which is based on a truncated prism - Leaving Cert DCG - Question A-1 - 2015
Step 1
Complete Plan and Elevation of the Cut Prism
Answer
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Complete Outline of Prism in Plan: Start by outlining the square base of the prism in the plan view. Draw the top face as a square and ensure to mark the oblique cut clearly.
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Use of Appropriate Solution Methodology: Ensure that the proper lines for the height of the prism are vertically aligned with the elevation view.
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Establish 2 Remaining Heights in Elevation: In the elevation view, identify and mark the heights for two surfaces cut by the oblique plane. You can use the given dimensions to accurately reflect these heights.
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Complete Elevation: Finally, draw the complete elevation view by connecting the established heights with straight lines to form a complete outline of the cut prism.
Step 2
Complete Pictorial Projection
Answer
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Establish 2 Required Heights in Pictorial Projection: For the pictorial view, determine the heights of the prism surfaces based on your previous elevation work. Clearly label these heights as they will guide the pictorial representation.
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Complete Pictorial Projection: With the heights established, proceed to draw the complete pictorial projection. Ensure that all three views (front, top, side) are represented accurately and in proportion.
Step 3
Determine the True Length of the Shorter Diagonal
Answer
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Identify Shorter Diagonal: Locate the shorter diagonal on the cut surface of the prism. This could be done by measuring the coordinates of the vertices involved on the cut face.
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Determine Correct True Length: To calculate the true length of the diagonal, apply the distance formula: d = rac{ ext{distance}}{ ext{cosine of the angle}} where the distance can be calculated using the coordinates of the endpoints of the diagonal based on the heights obtained earlier.