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The 3D graphic below shows a molecule of methane - Leaving Cert DCG - Question A-1 - 2011
Question A-1
The 3D graphic below shows a molecule of methane. The four outer atoms, shown in red, are located at the vertices of a tetrahedron. The drawing on the right shows t... show full transcript
Worked Solution & Example Answer:The 3D graphic below shows a molecule of methane - Leaving Cert DCG - Question A-1 - 2011
Step 1
Draw an auxiliary plan, on the given X,Y line, to show the dihedral angle between the planes abc and abd.
Answer
Step 1: Setting up the Auxiliary Plan
Begin by establishing the X,Y line on the drawing. This will serve as the reference line for your auxiliary plan.
Step 2: Projecting Points
From the elevation view of the tetrahedron, project the vertices of the triangular planes abc and abd perpendicular to the X,Y line. Mark these projections clearly.
Step 3: Transfer Distances
Ensure that the distances from each vertex of the tetrahedron to the X,Y line are accurately represented in the auxiliary plan.
Step 4: Determine Dihedral Angle
Using the projections of the planes abc and abd, calculate the dihedral angle. This can be done by determining the angle between the planes based on their normal vectors or using geometric relationships in the tetrahedron.
Step 2
Draw the projections of the largest possible sphere that can be contained inside the tetrahedron.
Answer
Step 1: Identify the Center
Locate the center of the tetrahedron, which can be defined as the centroid. This point will be the center of the largest inscribed sphere.
Step 2: Sphere Projection in Elevation
Draw a circle in elevation that represents the sphere. The radius can be defined based on the distance from the center to the closest face of the tetrahedron.
Step 3: Draw in Plan
Project the circle drawn for the sphere onto the auxiliary plan. Ensure it is tangent to each plane forming the tetrahedron.