Homework SourseSan Francisco International Airport uses giant steel ball be
San Francisco International Airport uses giant steel ball bearings built into each of the 267 columns which support the weight of the airport. Each ball bearing measures 5 feet in diameter with a maximum error of 0.01 feet. What is the maximum error for this diameter in computing the volume of this ball bearing?
Please show ALL steps/work involved!
Please show ALL steps/work involved!
Solution
volume of a sphere(v)=(4*pi*(r^3))/3
where r=radious of the sphere
let d=diameter of the sphere=r/2
puting the value of d in eqn (1) we will get
v=(pi*(d^3))dd/6
taking derivative on both sides,
dv=(pi*(d^2))dd/2
max change in volume=(pi(0.01^2))dd/2
=0.0000157 (ans)
