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The image below shows the Atomium structure, in Brussels, which is based on an inclined cube - Leaving Cert DCG - Question A-4 - 2016
Question A-4
The image below shows the Atomium structure, in Brussels, which is based on an inclined cube. The drawing on the right shows the incomplete projections of a similar... show full transcript
Worked Solution & Example Answer:The image below shows the Atomium structure, in Brussels, which is based on an inclined cube - Leaving Cert DCG - Question A-4 - 2016
Step 1
Complete the elevation of the cube.
Answer
To complete the elevation of the cube, follow these steps:
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Projection of vertices from plan to elevation: Begin by projecting each vertex from the plan view directly upward to its corresponding height in the elevation view.
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Transfer of heights from auxiliary view: Use the auxiliary view to establish the heights of the vertices. Ensure that all heights correspond to the vertical measurements taken from the plan.
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Draw outer edges of cube in elevation: Using the projected vertices and their established heights, draw the outer edges of the cube to form the main outline in the elevation view.
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Draw inner detail of cube in elevation: Lastly, include any inner details that provide a correct hidden detail of the cube, such as additional lines to denote internal structures or connections.
Step 2
Draw the plan and elevation of circumscribing sphere.
Answer
To draw the plan and elevation of the smallest circumscribing sphere:
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Establish centre of required sphere in elevation: Find the center of the cube in elevation, which will also be the center of the circumscribing sphere.
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Establish half of a true length of a 'body diagonal' to determine radius: Calculate the length of a body diagonal of the cube to find the radius of the sphere. The length of the body diagonal for a cube of side length 's' is given by the formula:
oot{3}$$. To find the radius, divide this length by 2:
oot{3}}{2}$$. 3. **Draw required sphere in elevation and plan**: Draw a circle in both the plan and elevation views that uses the calculated radius and centers at the established point.