Chapter 2.9, Problem 33E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

The circumference of a sphere was measured to be 84 cm with a possible error of 0.5 cm.

(a) Use differentials to estimate the maximum error in the calculated surface area. What is the relative error?

(b) Use differentials to estimate the maximum error in the calculated volume. What is the relative error?

To determine

**(a)**

**To estimate:**

The maximum possible error and the relative error in the calculated surface area, using differentials.

Explanation

**1) Formula:**

i. Surface area of a sphere is,

ii. The circumference of a sphere is,

iii. From the above expression,

iv. Relative error is calculated by dividing the maximum possible error by the total surface area:

**2) Given: **C = 84 cm and

**3) Calculation:**

To find maximum possible error in the calculated surface area express S as a function of C. We are given that the circumference of the sphere is 84 cm with possible error of 0.5cm.

Substitute

in

Now differentiate

with respect to C.

Multiply both sides by dC

Substitute C = 84 cm and

To determine

**b)**

**To estimate:**

The maximum possible error and the relative error in the calculated volume using differentials.

Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10E

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