PROBLEM 5: A plumb bob is shaped as cone with radius 3 cm and height 4 cm. The manufacturer specifiedthat the actual measurement of radius and height has uncertainties of 10.01 and ±0.005, respectively.Estimate the uncertainty in the actual volume of the plumb bob by applying differentials.

Answered: PROBLEM 5: A plumb bob is shaped as…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

A painting contractor charges Php 120 per sq.m. for painting the four walls and ceiling of a room. If the dimension of the ceiling are measured to be 4, and 5m, the height of the room is measured to be 3m, and these measurements are correct to 0.5cm, find approximately, by using total differential, the greatest error in estimating the cost of the job from theses measurements.
A cylindrical vessel without lid is 4 cm in radius and 10 cm in height. If the vessel is be coated with 0.4 cm of silver, use differentials to approximate the amount of silver to be used.
4. Water is draining from a cylindrical tank at 2.52 L/sec. Assume that the water tank has a diameter of 50 cm. How fast is the surface dropping?
A right circular cylinder was measured and the dimensions were found to be r = 15 cm and h = 7 cm. If the radius measurement has an uncertainty of 0.15 cm and the height measurement has an uncertainty of 0.1 cm, then estimate the maximum percentage error in the calculated volume. Recall the the percentage error is the amount of error divided by the calculated volume, dV in this case. (Also recall from the last problem that V = Trh and the total which is V differential here requires the product rule, resulting in dv = "(r²dh + 2rhdr) .) %

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PROBLEM 5: A plumb bob is shaped as cone with radius 3 cm and height 4 cm. The manufacturer specified that the actual measurement of radius and height has uncertainties of ±0.01 and 10.005, respectively. Estimate the uncertainty in the actual volume of the plumb bob by applying differentials.