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The 3D graphic below shows a Rubik's Cube and a display stand - Leaving Cert DCG - Question A-1 - 2013
Question A-1
The 3D graphic below shows a Rubik's Cube and a display stand. The drawing on the right shows the incomplete projections of the objects. (a) Complete the elevation ... show full transcript
Worked Solution & Example Answer:The 3D graphic below shows a Rubik's Cube and a display stand - Leaving Cert DCG - Question A-1 - 2013
Step 1
Complete the elevation of the cube.
Answer
Projection from Plan: Begin by constructing the necessary projection from the plan view of the Rubik's Cube. Identify and outline the edges, ensuring to capture the dimensions accurately.
Projection from Front View: The next step is to create the front view projection. Similar to the first step, ensure to mark the visible edges of the cube, adhering to prescribed measurements. This serves as a guide for wall thickness and articulation of the cube's structure.
Identification of Points in Elevation: Clearly define key points in the elevation that correspond to the various faces of the cube. This includes determining the vertex points that help in visualizing the cube's geometry in 3D.
Completion of Elevation: Using the identified points, proceed to complete the elevation drawing of the cube. This should show the top, sides, and bottom, including all visible faces, while accurately detailing the arrangement of colored squares on the cube's surface. Make sure to clearly illustrate the top face, which should display the coloration and layout of the cube.
Hidden Detail: Lastly, include any hidden lines that represent the internal structure of the Rubik's Cube. These lines are crucial in demonstrating the cube's volumetric characteristics effectively.
Step 2
Determine the diameter of the smallest possible sphere.
Answer
Identification of True Length of Body Diagonal: To calculate the diameter of the sphere that will encompass the cube, first find the true length of the body diagonal of the cube. This length can be computed using the formula for the body diagonal of a cube:
oot{3}$$ where $a$ is the length of a side of the cube. **Draw Required Sphere in End View**: Next, draw the sphere in the end view. The sphere should be centered about the cube, clearly demonstrating the smallest dimension that allows the entire cube to fit within. Make the diameter evident, and ensure that the drawing is to scale, maintaining proper proportions.