Select the correct answerWhile calculating the edge of a square,a worker makes an error of 2% in excess.What % error does he make in calculating area? (%)Options5%4.04%7%10%
Question
Select the correct answerWhile calculating the edge of a square,a worker makes an error of 2% in excess.What % error does he make in calculating area? (%)Options5%4.04%7%10%
Solution
The error in calculating the area of a square when there is an error in measuring the edge can be found using the formula for the area of a square (Area = edge^2) and the formula for percent error (Percent Error = |Approximate Value - Exact Value| / |Exact Value| * 100%).
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The worker makes an error of 2% in excess while calculating the edge of the square. This means the edge he measures is 102% of the actual edge.
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When he calculates the area, he squares this value. So, the area he calculates is (1.02)^2 = 1.0404 or 104.04% of the actual area.
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The percent error in the area is then |104.04 - 100| / 100 * 100% = 4.04%.
So, the worker makes a 4.04% error in calculating the area of the square. The correct answer is 4.04%.
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