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If an error of 1% is made in measuring the major and minor axes of an ellipse, then the percentage error in the area is approximately equal to
  • a)
    1%
  • b)
    2%
  • c)
    π%
  • d)
    4%
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If an error of 1% is made in measuring the major and minor axes of an ...
Let 2 a and 2 b be the major and minor axes of the ellipse
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Most Upvoted Answer
If an error of 1% is made in measuring the major and minor axes of an ...
Given:
- Error in measuring major and minor axes of an ellipse = 1%
- To find: Percentage error in the area of the ellipse

Solution:
Let us consider the formula for the area of an ellipse, which is given by:

Area = π * a * b

Where,
a = major axis of the ellipse
b = minor axis of the ellipse

Now, suppose the actual values of a and b are a1 and b1 respectively. But due to the error in measurement, the measured values are a2 and b2, which are different from the actual values.

Therefore, we can write:

a2 = a1 + (1% of a1) = 1.01*a1
b2 = b1 + (1% of b1) = 1.01*b1

Substituting these values in the formula for area, we get:

Area2 = π * a2 * b2
= π * (1.01*a1) * (1.01*b1)
= π * 1.0201 * a1 * b1

Now, let us consider the actual area of the ellipse, which is given by:

Area1 = π * a1 * b1

The percentage error in the area can be calculated as follows:

Percentage error = [(Area2 - Area1)/Area1] * 100%
= [(π * 1.0201 * a1 * b1 - π * a1 * b1)/ (π * a1 * b1)] * 100%
= (1.0201 - 1) * 100%
= 0.0201 * 100%
= 2.01%

Therefore, the percentage error in the area of the ellipse is approximately equal to 2%.

Hence, option B is the correct answer.
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