Some of this is just arithmetic . . .
The volume of the correct sphere is: .In a manufacturing process, ball bearings must be made with
with a maximum error in the radius of: .
Estimate the maximum error in the volume of the ball bearing.
Solution: The formula for the volume of the sphere is: .
If an error is made in measuring the radius of the sphere,
the maximum error in the volume is: .
With an error of , the radius is: .
And the volume is: .
The error in volume is: .
. . Hence: .
Rather than calculating , approximate with , where: .
Replacing with ,and with gives: .