Given:

• Formula to estimate the height: $H = 4F + 12$, where $F$ is the number of floors.
• The building has $F = 110$ floors.
• Real height of the building = 442 meters.

Step 1: Calculate the Estimated Height

Using the formula $H = 4F + 12$:

$H = 4 \times 110 + 12 = 440 + 12 = 452 \, \text{meters}.$

Step 2: Find the Difference Between the Estimated and Real Height

The difference is:

$\text{Difference} = 452 - 442 = 10 \, \text{meters}.$

Step 3: Calculate the Percentage of the Difference with Respect to the Real Height

The percentage difference is given by:

$\text{Percentage difference} = \left( \frac{\text{Difference}}{\text{Real height}} \right) \times 100 = \left( \frac{10}{442} \right) \times 100.$

Let's calculate this:

$\text{Percentage difference} \approx \left( \frac{10}{442} \right) \times 100 \approx 2.26\%.$

Rounding this to 1 decimal place gives:

$\text{Percentage difference} = 2.3\%.$

Since 2.3% is less than 5%, Seb's estimate is indeed within the required range.

Final Answer

The percentage difference is 2.3%.

Would you like further explanation or have any questions?

Related Questions

1. How would the formula change if the additional height per floor varied?
2. What would the estimated height be for a building with 200 floors using the same formula?
3. How sensitive is the percentage difference to changes in the number of floors?
4. What real-life factors could cause a difference between estimated and real building heights?
5. If a building's actual height is underestimated by 3%, how many meters would that be for a 600-meter tall building?

Tip

Always double-check percentage calculations by ensuring the ratio is taken relative to the correct "whole" (in this case, the real height).