The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.) cm2

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

To find :(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)

Since Area   square units

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  

Answerthe simplified expression isexplanationthe given expression is,let us deal with the bracket first.the two negatives in the parenthesis will become positive.the expression now becomes,we now expand the parenthesis to get,we group like terms to obtain,this simplifies to,

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