Answer:
Option (a) is correct.
Step-by-step explanation:
We know that area of the circle is [tex]\pi r^2[/tex] where r is the radius of the circle.
Let [tex]f(r)=\pi r^2[/tex]
Differentiate with respect to r
[tex]f'(r)=\pi 2r^{2-1}=2\pi r[/tex]
As [tex]r= 12 \,inches[/tex],
[tex]f'(12)=2\pi (12)=24\pi[/tex]
Also, its given that [tex]\Delta r=0.01\,\,inches[/tex]
We know that as per linear approximation to estimate the resulting error,
[tex]\Delta f(r)\approx f'(r)\,\Delta r[/tex]
Put [tex]f'(r)=24\pi\,,\,\Delta r=0.01 \,\,inches[/tex]
[tex]\Delta f(r)\approx f'(r)\,\Delta r\\=(24\pi)(0.01)\\=0.24\pi\,\,square \,\,inches[/tex]
Therefore,
the error is [tex]\pm 0.24\pi[/tex]
So, option (a) is correct.
