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A length is measured as 15.0 m with an uncertainty of ±0.3 m. If this length is

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Question: A length is measured as 15.0 m with an uncertainty of ±0.3 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?

Options:

  1. 9.0 m²
  2. 1.5 m²
  3. 0.9 m²
  4. 0.45 m²

Correct Answer: 0.9 m²

Solution: 

Area = length², maximum error = 2 * length * uncertainty = 2 * 15.0 * 0.3 = 9.0 m².

A length is measured as 15.0 m with an uncertainty of ±0.3 m. If this length is

Practice Questions

Q1
A length is measured as 15.0 m with an uncertainty of ±0.3 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
  1. 9.0 m²
  2. 1.5 m²
  3. 0.9 m²
  4. 0.45 m²

Questions & Step-by-Step Solutions

A length is measured as 15.0 m with an uncertainty of ±0.3 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
  • Step 1: Understand that the area of a rectangle can be calculated using the formula Area = length × length.
  • Step 2: Since the length is given as 15.0 m, we can write the area as Area = 15.0 m × 15.0 m.
  • Step 3: Calculate the area: Area = 15.0 m × 15.0 m = 225.0 m².
  • Step 4: Identify the uncertainty in the length, which is ±0.3 m.
  • Step 5: To find the maximum possible error in the area, we use the formula for error in area when using length: maximum error = 2 × length × uncertainty.
  • Step 6: Substitute the values into the formula: maximum error = 2 × 15.0 m × 0.3 m.
  • Step 7: Calculate the maximum error: maximum error = 2 × 15.0 × 0.3 = 9.0 m².
  • Uncertainty in Measurements – Understanding how to calculate the uncertainty in derived quantities based on the uncertainties of the measured quantities.
  • Area Calculation – Applying the formula for area and understanding how to propagate uncertainties through mathematical operations.
  • Error Propagation – Using the appropriate formula for maximum error when squaring a measured quantity.
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