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If the area of a rectangle is calculated as 50 m² with a length of 10 m and an u

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Question: If the area of a rectangle is calculated as 50 m² with a length of 10 m and an uncertainty of ±0.1 m in length, what is the uncertainty in the area?

Options:

  1. 1 m²
  2. 0.5 m²
  3. 0.2 m²
  4. 0.1 m²

Correct Answer: 0.5 m²

Solution: 

Uncertainty in area = 2 * length * uncertainty in length = 2 * 10 * 0.1 = 2 m².

If the area of a rectangle is calculated as 50 m² with a length of 10 m and an u

Practice Questions

Q1
If the area of a rectangle is calculated as 50 m² with a length of 10 m and an uncertainty of ±0.1 m in length, what is the uncertainty in the area?
  1. 1 m²
  2. 0.5 m²
  3. 0.2 m²
  4. 0.1 m²

Questions & Step-by-Step Solutions

If the area of a rectangle is calculated as 50 m² with a length of 10 m and an uncertainty of ±0.1 m in length, what is the uncertainty in the area?
  • Step 1: Identify the formula for the area of a rectangle, which is Area = Length × Width.
  • Step 2: In this case, we know the area is 50 m² and the length is 10 m.
  • Step 3: Since the width is not given, we can find it using the area formula: Width = Area / Length = 50 m² / 10 m = 5 m.
  • Step 4: Understand that the uncertainty in the area can be calculated using the formula: Uncertainty in Area = 2 × Length × Uncertainty in Length.
  • Step 5: Substitute the values into the formula: Uncertainty in Area = 2 × 10 m × 0.1 m = 2 m².
  • Step 6: Conclude that the uncertainty in the area is 2 m².
  • Area Calculation – Understanding how to calculate the area of a rectangle using the formula Area = Length × Width.
  • Propagation of Uncertainty – Applying the rules of uncertainty propagation to determine how uncertainties in measurements affect calculated results.
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