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The graphic on the right shows a modern Irish building structure - Leaving Cert DCG - Question C-3 - 2015
Question C-3
The graphic on the right shows a modern Irish building structure. Fig. C-3 below shows the plan and elevation (excluding hidden detail) of the structure. The outlin... show full transcript
Worked Solution & Example Answer:The graphic on the right shows a modern Irish building structure - Leaving Cert DCG - Question C-3 - 2015
Step 1
Draw the given plan and elevation of the structure.
Answer
To start, sketch a square outline representing the plan view of the building, ensuring each side is equal in length to maintain a proper square shape. Then, draw the elevation view showcasing the triangular roof. Make sure both the plan and elevation are to scale, as specified (Scale 1:200). Clearly label the dimensions shown in the provided figure.
Step 2
Determine the dihedral angle between the surfaces A and B.
Answer
Identify points A and B on the provided elevation. Use the line of intersection between surfaces A and B. The dihedral angle can be calculated using the angle between the projections of these surfaces. Measure the angle where the two planes intersect, ensuring the use of tools for accuracy.
Step 3
Draw the true shape of surface C and hence determine the radius of the largest circle that can be contained within the surface.
Answer
Create the true shape of surface C by projecting lines perpendicular to the respective edges. After the triangular outline is established, employ geometric methods to inscribe a circle within the triangle. The radius of the circle can be determined using the triangle's area and the semi-perimeter formula for inscribing a circle given by:
r = rac{A}{s}
where A is the area of the triangle, and s is the semi-perimeter.
Step 4
Determine the pitch of surface A.
Answer
The pitch can be calculated by measuring the vertical rise over the run of the surface A. The formula used to calculate the pitch (in degrees) is given by:
ext{Pitch} = an^{-1} rac{ ext{rise}}{ ext{run}}
Make sure to clearly show this calculation with the rise being the height of surface A and the run being the horizontal distance covered.
Step 5
Determine and indicate, in metres, the minimum length of cable required.
Answer
To find the total length of cable needed for the lightning conductor, calculate the distance from the apex of the building down through point P to point Q at the ground. This involves measuring the segments along the edges of the surface A, using the Pythagorean theorem if necessary for any diagonal lengths. Present the final calculated length in metres as per scale conversion.