In a manufacturing process, ball bearings must be made with radius of 0.4 mm, with a maximum error in the radius of ±0.013 mm. Estimate the maximum error in the volume of the ball bearing.
Solution: The formula for the volume of the sphere is________. If an error ∆r is made in measuring the radius of the sphere, the maximum error in the volume is ∆V=__________.
Rather than calculating ∆V, approximate ∆V with dV, where dV=__________.
Replacing r with___ and dr=∆r with ±____ gives dV= ±____.
The maximum error in the volume is about____mm^3.