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The graphic on the right shows a multimedia player for streaming TV over the Internet - Leaving Cert DCG - Question C-2 - 2014

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Question C-2

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The graphic on the right shows a multimedia player for streaming TV over the Internet. The hyperbolic parabolic shape on the top of the unit is designed to prevent u... show full transcript

Worked Solution & Example Answer:The graphic on the right shows a multimedia player for streaming TV over the Internet - Leaving Cert DCG - Question C-2 - 2014

Step 1

Draw the given plan of the hyperbolic parabolic surface ABCD.

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Answer

To draw the plan of the hyperbolic parabolic surface ABCD:

  1. Start by sketching a rectangle to represent the base of the surface.
  2. Label the corners as A, B, C, and D, following the outline provided.
  3. Mark the horizontal and vertical dimensions based on the projections:
    • The vertical dimensions from points B and D will reach 60 units and be symmetrical about the center line.
    • Mark the midpoints and divisions accordingly to indicate the curvature.

Step 2

Elements in plan (incl. division).

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Answer

In the plan view, to illustrate the elements and their divisions:

  1. Show a grid of lines dividing the surface into equal sections. This represents the elements of the surface.
  2. Ensure that the division matches the height of 55 units and mark additional lines at 30° and 60° inclined angles corresponding to the curvature.

Step 3

Draw the outline of surface in elevation.

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Answer

For the elevation:

  1. Begin with the vertical projection of ABCD.
  2. Highlight the curved outline as described in the image above.
  3. Indicate the heights, ensuring that the outward curvature resembles the hyperbolic section shown.

Step 4

Elements in elevation (incl. division or proj.).

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Answer

In the elevation view:

  1. Sketch the vertical divisions using lines that curve outward, reflecting the surface shape.
  2. Maintain consistency in spacing within the element divisions from A to C.

Step 5

Curve in elevation.

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Answer

Finally, for the curve in elevation:

  1. Draw the hyperbolic curve accurately using smooth lines.
  2. Indicate the part of the surface between points B and D with arrows to show flow and direction, capturing the essence of the hyperbolic shape.

Step 6

Determine heights and widths for surface ABCD.

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Answer

To determine the heights and widths:

  1. Identify the maximum height from point D or B, which is 60 units.
  2. The width, based on the end sections of ABCD, is indicated to be 55 units.

Step 7

Draw the outline of the hyperbolic paraboloid.

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Answer

Outline the hyperbolic paraboloid by:

  1. Creating a smooth curve connecting all identified points that depict the surface profile.
  2. Ensure the proportions reflect the actual dimensions derived from both plan and elevation.

Step 8

Draw the elements.

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Answer

Draw the elements of the surface:

  1. Mark horizontal lines through the newly established outline, parallel to the base rectangle.
  2. Add vertical lines that align with the previously drawn elevations and connect the points in three-dimensional form.

Step 9

Curve in end view.

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101 rated

Answer

To depict the curve in the end view:

  1. Show a gentle curve rising above the base A to B, indicating the hyperbolic section.
  2. Ensure the curvature looks realistic, matching the height perspectives from previous drawings.

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