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A terrarium is a glass container for soil and plants as shown - Leaving Cert DCG - Question C-3 - 2018

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Question C-3

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A terrarium is a glass container for soil and plants as shown. Fig. C-3 shows the plan and elevation of two geometric terrariums. The terrarium on the left is base... show full transcript

Worked Solution & Example Answer:A terrarium is a glass container for soil and plants as shown - Leaving Cert DCG - Question C-3 - 2018

Step 1

Draw the plan as given

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Answer

To begin, draw the base of the square pyramid with all sides measuring 20mm. Position the apex above the center of the base at a suitable height (e.g., 20mm) to represent the height of the pyramid accurately.

Step 2

Draw elevation as given

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Next, draw the elevation of the left-hand terrarium, ensuring the apex of the pyramid aligns with the base in the correct positioning.

Step 3

X1Y1 parallel to line of intersection

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Project lines from points A and B horizontally to create X1Y1, which should be parallel to the line where surfaces A and B intersect. Ensure precise measurements for accuracy.

Step 4

New X2Y2 perpendicular to line of intersection

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From the intersection, draw a new line X2Y2 that is perpendicular to the intersection line. Label this line clearly for reference.

Step 5

Projection of surfaces A and B as lines and indicating dihedral angle

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Finally, project surfaces A and B in line form, clearly indicating the dihedral angle between them. Label the angle accordingly, noting that it will involve measuring and calculating the angle formed.

Step 6

Construction to determine true shape of surface C

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Utilize the previously drawn outline for surface C. Construct the necessary triangles, ensuring that all sides and angles are congruent to maintain accuracy.

Step 7

Draw outer hexagon and diagonals in plan

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For the right-hand terrarium, begin with a hexagon outline of 150mm side length. Draw the diagonals of the hexagon to assist in elevation projections.

Step 8

Draw equilateral triangle base to complete plan

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Complete the plan view by drawing an equilateral triangle that connects appropriate points on the hexagon outline, clearly showing the shape as per the specifications.

Step 9

Use of semi-circle to determine orientation of cube in elevation

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To visualize the cube's orientation effectively, utilize a semi-circle to display the cube's height in elevation relative to the hexagonal base. This will clarify the relationship between both geometries.

Step 10

Complete elevation of terrarium

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Finally, project the elevation of the entire terrarium structure, ensuring all components are aligned accurately and labeled for clarity, completing the representation.

Step 11

X1Y1 inclined at 60° as shown

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Indicate that the line X1Y1 is inclined at an angle of 60°. This will serve as a reference for the shapes described in the following steps.

Step 12

Edge view of surface D to determine inclination to HP

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Construct the edge view of surface D, clearly demonstrating its inclination to the horizontal plane, providing visual evidence of its angle.

Step 13

Construction to determine true shape of surface D

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Answer

Conclude by constructing the true shape of surface D based on the angle and observations made in previous steps, ensuring all measurements are accurate and clear.

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