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The 3D graphic on the right shows a fireplace in the form of a semi-hyperboloid of revolution - Leaving Cert DCG - Question C-2 - 2012
Question C-2
The 3D graphic on the right shows a fireplace in the form of a semi-hyperboloid of revolution. The copper structure has been cut as shown to form the sloping top. A ... show full transcript
Worked Solution & Example Answer:The 3D graphic on the right shows a fireplace in the form of a semi-hyperboloid of revolution - Leaving Cert DCG - Question C-2 - 2012
Step 1
Draw the outline plan and elevation of the semi-hyperboloid of revolution, including the semi-circular base.
Answer
To draw the outline plan and elevation of the semi-hyperboloid of revolution, start by defining the base and support pillar based on the dimensions provided:
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Base and Support Pillar:
- Establish the dimensions (width and height).
- Ensure that the base is a semi-circle of radius 700 mm, and the pillar is 1200 mm wide.
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Hyperbolic Curves:
- Identify the height (2000 mm) and width (600 mm) for the hyperbolic curves.
- Compute the necessary points for the hyperbolic outline using standard equations for hyperbolas.
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Vertices:
- Mark the vertices based on the double hyperbola.
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Additional Points:
- Construct additional points on the curves to define the shape effectively, ensuring smooth connections.
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Draw Outline:
- Finally, draw the outline of the hyperbolic curves and the semi-circular base.
Step 2
Draw the projections of the sloping top in elevation and plan.
Answer
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Draw Sloping Top in Elevation:
- Begin by creating a 2D elevation drawing based on the dimensions of the sloping top.
- Use guidelines to ensure angles reflect the sloping nature accurately.
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Endpoints on Curve in Plan:
- Project sloping lines downward from the elevation to define where they meet on the plan view.
- Identify key points on the curve and join with a smooth line.
Step 3
Draw the projections of the vertical opening.
Answer
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Draw Vertical Opening in Plan:
- Indicate the vertical opening in the plan view of the fireplace, keeping the dimensions proportional.
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Endpoints on Curve in Elevation:
- In the elevation view, determine the endpoints of the curves corresponding to the vertical opening, ensuring they are aligned correctly.
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Additional Points in Plan and Draw Curve:
- Establish any additional points needed for accuracy and smoothness in both plan and elevation views, reflecting the actual structure.