Ceiling (slab underside) height from floor by levelling: A floor has RL = 99.995 m and the staff reading on the floor is 1.505 m. An inverted staff reading taken to the roof underside (slab) is 1.795 m. What is the floor-to-slab height?

Introduction / Context:Levelling can determine vertical clearances within buildings. Using a normal staff reading to the floor and an inverted staff reading to the slab, the ceiling height is obtained without directly measuring with ladders or tapes.

Given Data / Assumptions:

• RL_floor = 99.995 m.
• Staff reading on floor (upright) = 1.505 m.
• Inverted staff reading to slab underside = 1.795 m.
• Instrument level is unchanged between the two readings.

Concept / Approach:Height of instrument HI = RL_floor + staff_floor = 99.995 + 1.505 = 101.500 m. For an inverted staff reading r_inv, the RL of the roof underside is RL_roof = HI + r_inv (since the staff is upside down). Then the vertical clearance (height) = RL_roof − RL_floor.

Step-by-Step Solution:

Verification / Alternative check:A direct tape measurement should match 3.300 m within small error if measured plumb between the same two points.

Why Other Options Are Wrong:

• 3.290 m and 3.275 m: result from arithmetic slips or misinterpreting the inverted reading sign.
• 2.790 m: ignores the added inverted reading above HI.

Common Pitfalls:Treating inverted readings as subtractive; changing instrument height between the two shots; mixing units or truncating decimals incorrectly.

Final Answer:3.300 m