Question

find the percentage error in the area of an ellipse if 1% error is made in measuring the major and minor axes?

Answer 1

Given

• 1% error is made in measuring the major and minor axes

To find

• percentage error in the area of an ellipse

Solution

we are provided that the error that has crept during the measurement of the major as well as the minor axis of the ellipse is one percentage, and are asked to find the percentage error which would be reflected in the area of the ellipse when the given error filled measurements of major and minor axis are used.

if a is the major axis and b is the minor axis of the ellipse then we know that the area of the ellipse is given by the equation,

area, A = πab

∆a/a × 100 = 1%. (given)

∆b/b × 100 = 1% (given)

then the percentage error in the area of the ellipse,

∆A/A ×100 = ∆a/a × 100 + ∆b/b × 100

or, ∆A/A ×100 = 1 + 1

or, ∆A/A ×100 = 2%

Therefore the percentage error in the area of ellipse would be two percentage