Derivatives: Differential

In a manufacturing process, ball bearings must be made with radius of 0.5 mm, with a maximum error in the radius of ±0.019 mm. Estimate the maximum error in the volume of the ball bearing.

**Solution:** The formula for the volume of the sphere is __4/3r^3Pi__ . If an error D*r* is made in measuring the radius of the sphere, the maximum error in the volume is D*V*= __4(r+delta(r))^2pi-4^2pi__

Rather than calculating D*V*, approximate D*V* with *dV*, where *dV*=__ 4r^2Pidr__ .

Replacing *r* with__ 0.5__ and *dr*=D*r* with ±__ 0.019__ gives *dV*=± _______

The maximum error in the volume is about ________ mm3

**The text in red are the answers i got, and the ones that are blank i dont know how to do. Can anyone tell me if the answers i obtained are correct....?**