Hey Im having some trouble with differentials, i was wondering if anyone could help me with the problem below.
In a manufacturing process, ball bearings must be made with radius of 0.4 mm, with a maximum error in the radius of (plus or minus)0.015 mm. Estimate the maximum error in the volume of the ball bearing.
Solution: The formula for the volume of the sphere is ____________ (choice between 4/3r^2Pi , 4r^3Pi , 4/3r^3Pi , or 4r^2Pi). If an error(delta r) is made in measuring the radius of the sphere, the maximum error in the volume is (delta)V = ___________________ ( choice between 4/3(r+Delta(r))^2Pi-4/3r^2Pi, or 4(r+Delta(r))^3Pi-4r^3Pi, or 4/3(r+Delta(r))^3Pi-4/3r^3Pi, or 4(r+Delta(r))^2Pi-4r^2Pi).
Rather than calculating (delta)V, approximate (delta)V with dV, where dV= ___________________ (choice between 8/3rPidr , or 12r^2Pidr , or 4r^2Pidr , or 8rPidr).
Replacing r with ___________ and dr = (delta)r with (plus or minus) ___________ gives dV = (plus or minus) ___________________.
The maximum error in the volume is about ____________ mm^3
Thanks for the help!
In a manufacturing process, ball bearings must be made with radius of 0.4 mm, with a maximum error in the radius of (plus or minus)0.015 mm. Estimate the maximum error in the volume of the ball bearing.
Solution: The formula for the volume of the sphere is ____________ (choice between 4/3r^2Pi , 4r^3Pi , 4/3r^3Pi , or 4r^2Pi). If an error(delta r) is made in measuring the radius of the sphere, the maximum error in the volume is (delta)V = ___________________ ( choice between 4/3(r+Delta(r))^2Pi-4/3r^2Pi, or 4(r+Delta(r))^3Pi-4r^3Pi, or 4/3(r+Delta(r))^3Pi-4/3r^3Pi, or 4(r+Delta(r))^2Pi-4r^2Pi).
Rather than calculating (delta)V, approximate (delta)V with dV, where dV= ___________________ (choice between 8/3rPidr , or 12r^2Pidr , or 4r^2Pidr , or 8rPidr).
Replacing r with ___________ and dr = (delta)r with (plus or minus) ___________ gives dV = (plus or minus) ___________________.
The maximum error in the volume is about ____________ mm^3
Thanks for the help!
