The 3D graphic on the right shows the pop star Beyoncé and her notable engagement ring - Leaving Cert DCG - Question C-3 - 2013
Question C-3
The 3D graphic on the right shows the pop star Beyoncé and her notable engagement ring. The brilliance of the diamond is determined by the accuracy and symmetry of t... show full transcript
Worked Solution & Example Answer:The 3D graphic on the right shows the pop star Beyoncé and her notable engagement ring - Leaving Cert DCG - Question C-3 - 2013
Step 1
Draw the given plan of the diamond.
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Answer
To draw the given plan of the diamond, start by creating a square outline based on the measurements provided in Fig. C-3. Ensure that the proportions are accurate, as they will be crucial for the perspective of the diamond.
Step 2
Draw the elevation of the top portion of the diamond (surfaces B, C and E).
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Answer
For the elevation of the diamond, mark the surfaces B, C, and E accurately per the given 45° pitch. This elevation will help visualize the top section and align with the previously drawn plan.
Step 3
Determine the dihedral angle between surfaces A and B.
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The dihedral angle is defined by calculating the angle between the normals of surfaces A and B at the edge they share. Using geometric principles, one can utilize a protractor or trigonometric identities to find this angle mathematically.
Step 4
Complete the elevation of the diamond.
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To complete the elevation, apply the true length of the underside edges (9.5mm). Showcase the slope and ensure the correct placement of lower apex (2,2) as indicated. Accurate elevation is necessary for a comprehensive understanding of the diamond's structure.
Step 5
Determine the dihedral angle between the surfaces D and F.
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Answer
Similar to part (b), find the dihedral angle between surfaces D and F by evaluating the angle formed by the intersecting edges. Establish the normals for both surfaces and calculate the angle between them to determine the dihedral angle accurately.
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