Photo AI
A design for a patio fireplace based on a regular solid is shown - Leaving Cert DCG - Question A-3 - 2017
Question A-3
A design for a patio fireplace based on a regular solid is shown. The drawing shows the elevation and plan of a similar solid. All faces are regular pentagons. (a) ... show full transcript
Worked Solution & Example Answer:A design for a patio fireplace based on a regular solid is shown - Leaving Cert DCG - Question A-3 - 2017
Step 1
Using the given X,Y,Z, draw the true length of the line of intersection between faces A and B, and hence determine the dihedral angle between the two faces.
Answer
- Identify the positions of faces A and B: First, establish the orientation of faces A and B based on the elevation and plan drawings.
- Draw the line of intersection: Utilize the reference points X, Y, and Z to accurately sketch the true length of the line of intersection. Label the intersection clearly.
- Determine the dihedral angle: Measure the angle between the normal lines to the faces at the intersection. Use geometric principles to calculate the dihedral angle using the line of intersection and the normals of the two pentagonal faces.
Step 2
Determine the centropoint of face B in plan and draw the projections of a sphere which rests on the horizontal plane and is also in tangential contact with the centre point of face B.
Answer
- Locate the centropoint of face B: In the plan view, identify the center of face B by finding the midpoints of the edges and drawing lines accordingly.
- Draw projections for the sphere: From the centropoint, project vertical lines to represent the sphere resting on the horizontal plane.
- Ensure tangential contact: Make sure the radius is drawn such that the sphere is in tangential contact with the center point of face B, ensuring the correct projection onto both the horizontal plane and the vertical elevation.