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The circumference of a sphere was measured to be 84 $\mathrm{cm}$with a possible error of 0.5 $\mathrm{cm} .$(a) Use differentials to estimate the maximum error in thecalculated surface area. What is the relative error?(b) Use differentials to estimate the maximum error in thecalculated volume. What is the relative error?

A. Maximum Error in the calculated surface area is 27 $\mathrm{cm}^{2}$Maximum Relative Error $\approx 0.012$B. maximum error: 179 $\mathrm{cm}^{3} \quad$ relative error: 1.8$\%$

Calculus 1 / AB

Chapter 2

DERIVATIVES

Section 8

Linear Approximations and Differentials

Derivatives

Differentiation

Applications of the Derivative

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in this question, we are given the circumference of a sphere. Certainly not this circumference by thanks. And from this information, we know the Raiders office a free is given by X over two. Now, we want to talk about the volume and, uh, the theory area for the severe. So part of a issa Paula Boring. So the Valentino by Kendall v equals two. Um, sir, the pasta is actually the, uh, the area. So I did not kept away for the area, which, given by four pi r square and just replaced the radio The radius up in terms of X So we have full pi times x squared, divided by full pi square. So we have X square over pot. It's our, um, area And these different show you caused to two x over a pie The X Solan mix era, which is a A, which is to x the X divided by pi and the X and V X is giving in this program and they just Prague in those number. So don't forget, um, we have the on the unit Indian, so we used to use the calculator. We have this result 27 squares and Demeter and the full of relative era. We do the question d a over. Hey, the different show divided by ah, the original function. And we need to do some consolation before we plug in the values. So a because the X square over type you know, we have to two times the X divided by X. Now we can just plug in the X and the X. Given my giving, the problem reaches around 0.12 And for property we grow sending that we replace a by the which with the volume. So we for severe because toe 43 pi r cubed and then remember our I closed toe X over two pies. It's for three times times X cubed over eight pike you which is X cubed over a six pi square in the end sort of different show you coast to X square over two pi square PXE Not for the Mex era Again we plug in the value off X and V X Even in a program we have 84 square times to your 840.5 divided by two pi square. It's around 17 117. I aren't your big sentiment. Er so don't forget we have this unit and the relative Hera. It's given by TV, divided by V. So we again we go some consolation before we probably in the value for X and P X. So we have three d x over x Simeon. And now we can just plug in the values for external yanks. So we have 0.18 and their percentage herro just converse. This result to be a percent 1.8%. And we do the same thing for this, uh, for this area. So for the area, the percentage very close to 1.2%.

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