Posted by **Steven** on Friday, December 4, 2009 at 5:08am.

Suppose a cylindrical can is manufactured with radius r. The manufacturing process makes the length r imprecise; r can be off by ±0.03 cm. The manufacturing process makes the height of the can precisely equal to three times the radius r (including any error in r, but not introducing any new error).

a) Use ∆r= ±0.03 to approximate the corresponding error in the volume of the can by using differentials (or the linear approximation)

b) The fraction ∆r/r is called the relative error of percentage error in the radius. If the relative error in the radius is z, approximate the corresponding relative error in the volume.

- Calculus -
**drwls**, Friday, December 4, 2009 at 6:15am
V = pi r^2 h = pi r^2 * 3r = 3 pi r^3

(a) If r becomes r + ∆r ,

V + ∆V = 3 pi (r + ∆r)^3

=3 pi [r^3+ 3r^2 ∆r + 3r(∆r)^2 + (∆r)^3]

V [1 +3(∆r)/r +3(∆r)^2/r^2 +(∆r)^3/r^3]

Since ∆r/r <<1, this linearizes to

V(1 + 3 ∆r/r)

So ∆V = 3V *(∆r/r)

(b) ∆V/V = 3z

## Answer This Question

## Related Questions

- Accounting - Cherry Hill Glass Company employs a normal costing system. The ...
- Accounting - Cherry Hill Glass Company employs a normal costing system. The ...
- Manufacturing process - Product that using manufacturing process and its process...
- Manufacturing Process - List three benefits of the laser welding process.
- accounting - To reconcile total manufacturing costs with the total cost of goods...
- math - the diameters of ball bearings produced in a manufacturing process can be...
- Manufacturing Process - Write out the full name of and list three properties of ...
- Accounting 10 PLEASE HELP ME! - Oscar Corp. applies manufacturing overhead to ...
- Accounting 10 - Oscar Corp. applies manufacturing overhead to production at 150...
- Accounting 1 - Oscar Corp. applies manufacturing overhead to production at 150% ...

More Related Questions