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The 3D graphic, and enlarged balloon detail on the right, show a cooker hood in a kitchen - Leaving Cert DCG - Question C-3 - 2010
Question C-3
The 3D graphic, and enlarged balloon detail on the right, show a cooker hood in a kitchen. Fig. C-3 below shows the plan and elevation of the cooker hood. Surfaces ... show full transcript
Worked Solution & Example Answer:The 3D graphic, and enlarged balloon detail on the right, show a cooker hood in a kitchen - Leaving Cert DCG - Question C-3 - 2010
Step 1
Draw the given plan and elevation.
Answer
To draw the plan and elevation of the cooker hood:
- Start with the rectangular base, ensuring it measures 500 mm across and 350 mm down as per the elevation.
- Draw surface B as a trapezoid, ensuring it is sloped at 40°.
- For surface A, draw it sloping at 45° from the top of surface B.
- Finally, incorporate surface C with appropriate dimensions leading to the cylinder D on top.
Step 2
Find the dihedral angle between surfaces A and B.
Answer
The dihedral angle between surfaces A and B can be derived using the angle of inclination.
- Surface A forms a 45° angle with the horizontal, and surface B forms a 40° angle.
- The dihedral angle θ can be calculated using the formula:
- Thus, the dihedral angle between the two surfaces is 85°.
Step 3
Draw a one-piece surface development of surfaces B and C.
Answer
To develop surfaces B and C:
- Start with the rectangular base for surface B up to the points where it slopes up.
- Continue the development around the trapezoidal part of surface B.
- For surface C, develop it at the specified 45° angle from point where surface B ends, ensuring it adheres to the dimensions outlined in the provided plan.
Step 4
Draw the development of the curved surface of the cylinder D.
Answer
To develop the curved surface of the cylinder D:
- Measure the circumference of the base of cylinder D, which is the same as the circular top.
- Calculate the development length based on the radius of the cylinder.
- Draw a rectangle with width equal to the circumference calculated, and height equal to the cylinder's height of 175 mm.
- The ends can be shown curved to finalize the development.