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 ∆ris made in measuring the radius of the sphere, the maximum error in the volume is ∆V=__________.

Rather than calculating ∆V, approximate ∆VwithdV, wheredV=__________.

Replacingrwith___ anddr=∆rwith ±____ givesdV= ±____.

The maximum error in the volume is about____mm^3.