Answer:
The Maximum error is
Step-by-step explanation:
Given that the circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm
<h3>To find :</h3><h3>(a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.)Given circumference of a sphere=82 cm and possible error =0.5 cm
Error of the surface area is dA
Error of circumference is dC = 0.5 cm
We know that the formula for Circumference of a sphere is C=2πr units
Differentiating with respect to r
(∵ dC = 0.5 cm)
Differentiating with respect to r
square units
Since given C = 82 cm.and also C=2πr we have
From that
Substituting the values of r and dr in the above equation we get
∴ Maximum error is