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The image below shows a paper weight - Leaving Cert DCG - Question A-1 - 2020
Question A-1
The image below shows a paper weight. It consists of a cube and a square prism which intersect each other. The drawing shows an incomplete dimetric projection of the... show full transcript
Worked Solution & Example Answer:The image below shows a paper weight - Leaving Cert DCG - Question A-1 - 2020
Step 1
Complete the dimetric projection of the paper weight.
Answer
To complete the dimetric projection of the paper weight:
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Location of points 'e' and 'f': Determine the vertical edges of the square prism. The points should reflect their correct positions corresponding to the cube.
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Complete surface 'abcd': Draw the faces connecting points a, b, c, and d, ensuring the angles mirror a cube's dimensional proportions.
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Location of points 'g' and 'h': Identify the location of points g and h based on the square prism's vertical edges.
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Complete surface 'bcgh': Connect the points b, c, g, and h to form a solid surface, maintaining correct geometric relations.
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Complete surface of the square prism: Finally, close the square prism by connecting points f, g, h, and suitable references to c, completing the projection.
Step 2
Determine, and indicate in degrees, the true angle between the surface 'abcd' and the H.P.
Answer
To determine the true angle between the surface 'abcd' and the horizontal plane (H.P.):
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Identify the normals: Determine the normal vector to the surface 'abcd'. This can be facilitated by calculating the cross product of vectors along the surface.
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Calculate the angle: Use the formula for calculating the angle between two planes: heta = an^{-1} rac{h}{d} where h is the perpendicular height from the surface to the H.P. and d is the distance from the edge on the H.P.
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Indicate the angle: Clearly label this angle in degrees on your projection diagram for clarity.