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The image on the right shows a wooden watch face - Leaving Cert DCG - Question C-2 - 2019

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Question C-2

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The image on the right shows a wooden watch face. The top surface of the watch face is a hyperbolic paraboloid. The watch face is a square in plan. (a) Draw the giv... show full transcript

Worked Solution & Example Answer:The image on the right shows a wooden watch face - Leaving Cert DCG - Question C-2 - 2019

Step 1

Outline of surface ABCD in plan

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Answer

To outline surface ABCD in plan, start by marking the coordinates A, B, C, and D. Connect these points to form a square, where each side measures 100 units, as indicated. Ensure that the square is perfectly symmetrical.

Step 2

Elements in plan (incl. division)

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Divide the square ABCD into equal sections. Given the scale of 1:1, mark grid lines extending from A to B, B to C, C to D, and D to A. Include additional divisions diagonally to emphasize the parabolic surface.

Step 3

Outline surface in elevation

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Answer

To outline the hyperbolic paraboloid in elevation, draw a curve that represents the parabolic shape from points A to D at the specified heights. Ensure symmetry along the central axis, making the transition smooth and continuous.

Step 4

Elements in elevation (incl. division or proj.)

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In the elevation, include horizontal divisions across the parabolic surface. These divisions should represent changes in elevation, visually enhancing the parabolic shape.

Step 5

Completion of elevation (curve and hidden detail)

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Finalize the elevation by refining the curves and adding hidden lines where necessary. This detail ensures clarity in understanding the depth of the hyperbolic surface.

Step 6

Determine heights and widths for surface ABCD

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Heights and widths of surface ABCD can be determined by identifying specific height values at points A, B, C, and D where they intersect the parabolic curve, ensuring they align with the given dimensions.

Step 7

Draw the outline of hyperbolic paraboloid surface

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Sketch the hyperbolic paraboloid surface using the previously determined heights and widths. This outline will include the necessary curvature to represent the parabolic shape accurately.

Step 8

Draw elements

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Represent the elements of the parabolic surface by plotting grid lines and additional curves that emphasize the 3D form of the hyperbolic paraboloid.

Step 9

Completion of end view (curve and hidden detail)

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Complete the end view by ensuring all curves are drawn smoothly, with hidden details represented where applicable. This gives a comprehensive view of the overall parabolic structure.

Step 10

Presentation

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Answer

Ensure the final presentation is neat and well-structured. Use appropriate shading and line weights to highlight the parabolic surface and provide clarity to the elevations and plans.

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