Answer:
[tex]\pm 9in^2[/tex]
Step-by-step explanation:
We are given that
Radius of end of a log, r= 9 in
Error, [tex]\Delta r=\pm 1/2[/tex]in
We have to find the error in computing the area of the end of the log by using differential.
Area of end of the log, A=[tex]pi r^2[/tex]
[tex]\frac{dA}{dr}=2\pi r[/tex]
[tex]\frac{dA}{dr}=2\pi (9)=18\pi in^2[/tex]
Now,
Approximate error in area
[tex]dA=\frac{dA}{dr}(\Delta r)[/tex]
Using the values
[tex]dA=18\pi (\pm 1/2)[/tex]
[tex]\Delta A\approx dA=\pm 9in^2[/tex]
Hence, the possible propagated error in computing the area of the end of the log[tex]=\pm 9in^2[/tex]
