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# As you eat your way through a bag of chocolate chip ISBN: 9780321675460 31

## Solution for problem 59P Chapter 1

University Physics | 13th Edition

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Problem 59P

As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 ± 0.02 cm and a thickness of 0.050 ± 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio of the diameter to the thickness and the uncertainty in this ratio.

Step-by-Step Solution:

Solution 59P Step 1 The volume of a cylindrical disc is given by V = r d2 Where r is the radius of the disc and t is the thickness. In this given problem we have d (8.50±0.02 cm) r = 2 = 2 = 4.25 ± 0.01 cm And t = 0.050 ± 0.005 cm So the volume is 4 2 2 3 V = r3t = (4.25 cm) (0.050 cm) = 2.84 cm Step 2 Now the relative error in radius is r 0.01 r = 4.25= .002 And relative error in thickness is t= 0.005 c= 0.1 t 0.050 cm So the relative error in the volume is V = 2 r + t= 2(0.02) + 0.1 = 0.14 V r t Hence absolute error in volume is V = V × (0.14) = (2.84 cm )(0.14) = 0.4 cm 3 Hence the volume with its uncertainty can be reported as V = 2.8 ± 0.4 cm 3

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##### ISBN: 9780321675460

This textbook survival guide was created for the textbook: University Physics, edition: 13. Since the solution to 59P from 1 chapter was answered, more than 284 students have viewed the full step-by-step answer. This full solution covers the following key subjects: cookie, Volume, uncertainty, thickness, ratio. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The full step-by-step solution to problem: 59P from chapter: 1 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. University Physics was written by and is associated to the ISBN: 9780321675460. The answer to “As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 ± 0.02 cm and a thickness of 0.050 ± 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio of the diameter to the thickness and the uncertainty in this ratio.” is broken down into a number of easy to follow steps, and 67 words.

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