Question

When the errors of 2% and 3% are made in measuring its major and minor

axes of ellipse respectively then the percentage error in the area of an

ellipse is

a) 4 % b) 5 % c) 3 % d) 1 %​

Answer 1

Answer:

5 b one is the correct way to anewer

Answer 2

Answer:

The percentage error in the area of an ellipse is b) 5%

Step-by-step explanation:

The area of the ellipse is given by A = πab

Here a represents the major axis and b represents the minor axis

The percentage error in the major axis is da/a = 2%

The percentage error in the minor axis is db/b =  3%

Now using the error analysis method

consider,

A = πab

Taking log on both sides

log(A) = logπ + log(a) + log(b)

differentiate both sides

$\frac{dA}{A} =0+\frac{da}{a} +\frac{db}{b}$

dA/A = 0 + 2% + 3%

dA/A = 5%

Therefore the percentage error in the area of an ellipse is 5%