A length is measured as 100.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the uncertainty in the area?
Practice Questions
1 question
Q1
A length is measured as 100.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the uncertainty in the area?
1 m²
0.5 m²
2 m²
0.25 m²
Area = L², so uncertainty in area = 2 * L * (uncertainty in L) = 2 * 100 * 0.5 = 100 m².
Questions & Step-by-step Solutions
1 item
Q
Q: A length is measured as 100.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the uncertainty in the area?
Solution: Area = L², so uncertainty in area = 2 * L * (uncertainty in L) = 2 * 100 * 0.5 = 100 m².
Steps: 7
Step 1: Understand that the area of a square is calculated using the formula Area = L², where L is the length of one side of the square.
Step 2: Identify the given length, which is 100.0 m.
Step 3: Identify the uncertainty in the length, which is ±0.5 m.
Step 4: To find the uncertainty in the area, use the formula for uncertainty in area: uncertainty in area = 2 * L * (uncertainty in L).
Step 5: Substitute the values into the formula: uncertainty in area = 2 * 100.0 m * 0.5 m.
Step 6: Calculate the result: 2 * 100 * 0.5 = 100 m².
Step 7: Conclude that the uncertainty in the area is ±100 m².
