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The image on the right shows the Hooker sculpture in Eye Square Galway - Leaving Cert DCG - Question B-1 - 2022
Question B-1
The image on the right shows the Hooker sculpture in Eye Square Galway. The geometry of the design comprises a series of planar surfaces. Fig. B-1 shows the plan an... show full transcript
Worked Solution & Example Answer:The image on the right shows the Hooker sculpture in Eye Square Galway - Leaving Cert DCG - Question B-1 - 2022
Step 1
Draw the given elevation and plan of the intersecting planes ABC, ABD and EFG.
Answer
- Start by marking the coordinates for points A, B, C, D, E, and F as provided.
- Create the elevation view by plotting the heights of each point based on the given vertical coordinates.
- For plane ABC, connect points A, B, and C to form the triangular elevation.
- For plane ABD, connect points A, B, and D to form the next triangular elevation.
- For plane EFG, connect points E, F, and G, ensuring the parallel edges BD and FG are correctly represented.
- Ensure all points are labeled clearly in the drawing for proper identification.
Step 2
Determine the dihedral angle between the planes ABC and ABD.
Answer
- Identify line AB as the common edge between planes ABC and ABD.
- Construct lines extending from point C to the normal line of plane ABC and from point D to the normal of plane ABD.
- Measure the angle between these two normals using a protractor to find the dihedral angle.
Step 3
Draw the elevation and plan of a horizontal line on the surface EFG and project an auxiliary elevation which will show an edge view of the plane EFG.
Answer
- Begin by drawing a horizontal line on the EFG plane in both the elevation and plan views.
- Project this line upwards to the auxiliary view.
- Determine the point where this line intersects the edge of plane EFG to illustrate the edge view.
- Clearly label the projection in the auxiliary view.
Step 4
Locate the projection of point P on the plane EFG which is a distance of 40mm from the horizontal plane and 68mm from the vertical plane.
Answer
- Mark the height of point P as 40mm above the horizontal plane.
- Measure 68mm horizontally from the vertical plane towards the EFG plane to determine the projection of point P.
- Project the determined point onto the plane EFG and indicate its position clearly in the drawing.
Step 5
Determine and indicate the true length of FP.
Answer
- Use the coordinates of point F and the newly located point P to calculate the length of line FP using the distance formula:
- Substitute the coordinates for P and F to gain the true length.
- Clearly mark the true length on the diagram next to line FP.