EXAMPLE 4The radius of a sphere was measured and found to be 23 cm with a possible error in measurement of at most 0.02 cm. What is themaximum error in using this value of the radius to compute the volume of the sphere?SOLUTIONIf the radius of the sphere is r then its volume is V =If the error in the measured value of r is denoted by dr = Ar, then thecorresponding error in the calculated value of V is AV, which can be approximated by the differentialdV = 4rrdr.When r = 23 and dr = 0.02, this becomesdV =4x((round to the nearest integer).The maximum error in the calculated volume is aboutcm3.

Given: Radius of sphere =23 cm Error in radius = dr = 0.02 Volume of sphere = V=43πr3

EXAMPLE 4 The radius of a sphere was measured and found to be 23 cm with a possible error in measurement of at most 0.02 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere? SOLUTION If the radius of the sphere is r then its volume is V = ar. If the error in the measured value of r is denoted by dr = Ar, then the %3D corresponding error in the calculated value of V is AV, which can be approximated by the differential dV = 4xr dr. When r= 23 and dr = 0.02, this becomes dV = 4x( (round to the nearest integer). The maximum error in the calculated volume is about cm3.

EXAMPLE 4 The radius of a sphere was measured and found to be 23 cm with a possible error in measurement of at most 0.02 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere? SOLUTION If the radius of the sphere is r then its volume is V = ar. If the error in the measured value of r is denoted by dr = Ar, then the %3D corresponding error in the calculated value of V is AV, which can be approximated by the differential dV = 4xr dr. When r= 23 and dr = 0.02, this becomes dV = 4x( (round to the nearest integer). The maximum error in the calculated volume is about cm3.

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

EXAMPLE 4
The radius of a sphere was measured and found to be 23 cm with a possible error in measurement of at most 0.02 cm. What is the
maximum error in using this value of the radius to compute the volume of the sphere?
SOLUTION
If the radius of the sphere is r then its volume is V =
If the error in the measured value of r is denoted by dr = Ar, then the
corresponding error in the calculated value of V is AV, which can be approximated by the differential
dV = 4rr
dr.
When r = 23 and dr = 0.02, this becomes
dV =
4x(
(round to the nearest integer).
The maximum error in the calculated volume is about
cm3.

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