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An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
- a)2%
- b)2.02%
- c)4%
- d)4.04%
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
An error 2% in excess is made while measuring the side of a square. Th...
100 cm is read as 102 cm.
∴ A1 = (100 × 100) cm2 and
A2 = (102 × 102) cm2.
(A2 – A1) = [(102)2 – (100)2]
= (102 + 100) × (102 – 100)
= 404 cm2
∴ Percentage error
= [404/(100 × 100) × 100]% = 4.04%
∴ A1 = (100 × 100) cm2 and
A2 = (102 × 102) cm2.
(A2 – A1) = [(102)2 – (100)2]
= (102 + 100) × (102 – 100)
= 404 cm2
∴ Percentage error
= [404/(100 × 100) × 100]% = 4.04%
Most Upvoted Answer
An error 2% in excess is made while measuring the side of a square. Th...
Understanding the Problem
When measuring the side of a square, an error of 2% in excess means the measured side is slightly longer than the actual side. We need to determine how this error affects the calculated area of the square.
Calculating the Area
1. Actual Side Length: Let the actual side length be "s".
2. Measured Side Length: With a 2% excess error, the measured side length becomes:
- Measured side = s + 0.02s = 1.02s.
3. Area Calculation:
- Actual Area = s^2.
- Measured Area = (1.02s)^2 = 1.0404s^2.
Finding the Percentage Error in Area
1. Error in Area:
- Error = Measured Area - Actual Area = 1.0404s^2 - s^2 = 0.0404s^2.
2. Percentage Error:
- Percentage Error = (Error / Actual Area) × 100
- Percentage Error = (0.0404s^2 / s^2) × 100 = 4.04%.
Conclusion
The percentage of error in the calculated area of the square due to a 2% excess error in measuring the side is 4.04%.
Thus, the correct answer is option 'D'.
When measuring the side of a square, an error of 2% in excess means the measured side is slightly longer than the actual side. We need to determine how this error affects the calculated area of the square.
Calculating the Area
1. Actual Side Length: Let the actual side length be "s".
2. Measured Side Length: With a 2% excess error, the measured side length becomes:
- Measured side = s + 0.02s = 1.02s.
3. Area Calculation:
- Actual Area = s^2.
- Measured Area = (1.02s)^2 = 1.0404s^2.
Finding the Percentage Error in Area
1. Error in Area:
- Error = Measured Area - Actual Area = 1.0404s^2 - s^2 = 0.0404s^2.
2. Percentage Error:
- Percentage Error = (Error / Actual Area) × 100
- Percentage Error = (0.0404s^2 / s^2) × 100 = 4.04%.
Conclusion
The percentage of error in the calculated area of the square due to a 2% excess error in measuring the side is 4.04%.
Thus, the correct answer is option 'D'.
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An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:a)2%b)2.02%c)4%d)4.04%Correct answer is option 'D'. Can you explain this answer?
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