Hello, nch!

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: .