the area of the circle was measured to be 29/30 of it original area.find the percentage error made in measuring area.
To find the percentage error made in measuring the area of the circle, we need to compare the difference between the measured area and the original area.
Let's denote the original area of the circle as A and the measured area as B. According to the given information, B is 29/30 of A.
So, B = (29/30) * A
To find the difference between the measured area and the original area, we subtract B from A:
Difference = A - B
Since we want the percentage error, we need to express the difference as a percentage of the original area, A.
Percentage error = (Difference / A) * 100
Now substitute the values:
Percentage error = ((A - B) / A) * 100
Percentage error = ((A - (29/30 * A)) / A) * 100
Simplifying further:
Percentage error = ((A - (29A/30)) / A) * 100
Percentage error = (((30A - 29A) / 30A)) * 100
Percentage error = ((A / 30A) * 100
Percentage error = (1/30) * 100
Therefore, the percentage error made in measuring the area of the circle is approximately 3.33%.