What is the uncertainty in the measurement of a length of 5.00 cm ± 0.02 cm when

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Question: What is the uncertainty in the measurement of a length of 5.00 cm ± 0.02 cm when calculating the area?

Options:

Correct Answer: 0.10 cm²

Solution:

Area = length² = (5.00 cm)² = 25.00 cm². The uncertainty in area is calculated using the formula: ΔA = 2LΔL = 2(5.00 cm)(0.02 cm) = 0.20 cm².

What is the uncertainty in the measurement of a length of 5.00 cm ± 0.02 cm when calculating the area?

What is the uncertainty in the measurement of a length of 5.00 cm ± 0.02 cm when calculating the area?

Step 1: Identify the length measurement, which is 5.00 cm.
Step 2: Identify the uncertainty in the length measurement, which is ± 0.02 cm.
Step 3: Calculate the area using the formula for area of a square: Area = length².
Step 4: Substitute the length into the formula: Area = (5.00 cm)².
Step 5: Calculate the area: Area = 25.00 cm².
Step 6: To find the uncertainty in the area, use the formula: ΔA = 2LΔL.
Step 7: Substitute the values into the uncertainty formula: ΔA = 2(5.00 cm)(0.02 cm).
Step 8: Calculate the uncertainty: ΔA = 0.20 cm².

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