Question

A student is trying to determine the flatness and parallelism of the top surface of a part whose cross-section, assumed uniform in the Z direction, is shown in the figure.
Which ONE of the following options is CORRECT?

• A. \( a \) is flatness while \( b \) is parallelism.
• B. \( a \) is parallelism while \( b \) is flatness.
• C. \( a + b \) is parallelism while \( b - a \) is flatness.
• D. \( a + b \) is flatness while \( b - a \) is parallelism.

Hint:

Ask which tolerance zone needs the Datum to be drawn. Flatness never references a datum; parallelism always does.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The figure shows two versions of the same wavy, slightly uneven top surface sitting on a flat bottom, called the Datum.
In one version, a tolerance band labeled \( a \) is drawn snug around the wavy surface itself, tilted to whatever angle best fits that surface.
In the other version, a tolerance band labeled \( b \) is drawn as two lines that stay strictly parallel to the bottom Datum surface.
We must decide which band represents flatness and which represents parallelism.

Step 2: Recalling the definitions of flatness and parallelism:
Flatness is a form tolerance. It only asks how much a surface deviates from being a perfect plane, and it does not care about any other surface or Datum at all.
Parallelism is an orientation tolerance. It asks how well a surface stays parallel to a stated reference Datum, so the tolerance zone is always fixed at a constant distance from that Datum, not tilted to fit the surface.

Step 3: Identifying zone \( a \):
Zone \( a \) is drawn tilted, following the general slope of the wavy top surface, and it makes no reference to the bottom Datum line at all.
Since it only measures how much the surface itself wanders from its own best fit plane, ignoring the Datum, zone \( a \) is the flatness tolerance zone.

Step 4: Identifying zone \( b \):
Zone \( b \) is drawn as two lines that are forced to stay parallel to the Datum surface below, at a fixed offset.
Because this tolerance zone is locked to the orientation of the Datum rather than to the surface's own best fit, zone \( b \) is the parallelism tolerance zone.

Step 5: Checking the options:
Option (A) says a is flatness while b is parallelism, which matches our identification exactly.
Option (B) reverses the two, which is incorrect since a has no Datum reference and cannot be parallelism.
Option (C) and Option (D) invent combined quantities like a+b and b-a, but flatness and parallelism are each defined by a single tolerance zone on the actual surface, not by adding or subtracting two zone widths, so both are incorrect.

Final Answer:
Zone a, which ignores the Datum, is flatness, and zone b, which is fixed parallel to the Datum, is parallelism. \[ \boxed{\text{Option (A)}} \]