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The 3D graphic on the right shows a cufflink which includes a hyperbolic paraboloid surface - Leaving Cert DCG - Question C-2 - 2013
Question C-2
The 3D graphic on the right shows a cufflink which includes a hyperbolic paraboloid surface. Fig. C-2 shows the plan and elevation of a typical hyperbolic paraboloi... show full transcript
Worked Solution & Example Answer:The 3D graphic on the right shows a cufflink which includes a hyperbolic paraboloid surface - Leaving Cert DCG - Question C-2 - 2013
Step 1
Draw the given plan and elevation of the hyperbolic paraboloid surface.
Answer
To draw the plan and elevation of the hyperbolic paraboloid surface ABCD, start with the elevations where the point C is the vertex.
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Outline of surface ABCD in plan: Draw a contour that represents the hyperbolic paraboloid based on the given dimensions in Figure C-2. The plan should reflect the coordinates of the points A (0, 0), B (100, 0), C (50, 30), and D (0, 30).
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Elements in plan (incl. division): Include relevant grid lines that represent the symmetry and curvature of the paraboloid. Ensure to showcase the divisions clearly on the plan view.
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Outline of surface ABCD in elevation: In the elevation view, again plot points A, B, C, and D to maintain the relationship with the plan view, emphasizing the 45-degree angles as per the depiction.
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Elements in elevation (incl. division or proj.): Similar to the plan view, draw grid lines and divisions in the elevation to indicate height and curvature.
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Curve in elevation: Finally, ensure that the curve representing the hyperbolic paraboloid is accurately depicted, following the outlines and dimensions provided.
Step 2
Project an end view of the hyperbolic paraboloid surface.
Answer
To project the end view of the hyperbolic paraboloid surface:
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Determine heights and widths for surface ABCD: Use the height from the elevation view (76 units high at C) and project to calculate the dimensions across the width at point C (30 units wide as per the given data).
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Draw the outline of the hyperbolic paraboloid: Create the outline showing the hyperbolic shape, beginning from the vertex based on the determined heights and widths.
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Draw the elements: Incorporate grid lines to provide a clearer structure to the hyperbolic profile which may indicate curves and divisions at appropriate intervals.
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Curve in end view: Illustrate the curve in the end view accurately to reflect the parabolic nature of the shape as seen from this perspective, ensuring that it transitions smoothly from the vertex outwards.
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Presentation: Ensure the projection is clean and well-presented, with clear annotations where necessary to communicate the dimensions and curvature effectively.