# Dimensions of a closed rectangular box

1. Oct 1, 2005

### Whatupdoc

The dimensions of a closed rectangular box are measured as 70 centimeters, 50 centimeters, and 100 centimeters, respectively, with the error in each measurement at most .2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.

V = LWH

dv = (WH)*DL + (LH)*DW + (LW)*DH
dv = (50)(100)(.2) + (70)(100)(.2)+(70)(50)(.2) = 3100 square centimeters

but the answer is incorrect. am i missing something?

2. Oct 1, 2005

### Tide

The problem is asking for error in calculating the surface area but you're doing volume and mysteriously changing the units to cm^2.

3. Oct 1, 2005

### Whatupdoc

Surface Area of a Rectangular = 2xy + 2yh + 2xh

DV = (2y)(dx) + (2h)(dy) + (2x)(dh)
(2)(50)(0.2) + (2)(100)(0.2)+(2)(70)(0.2) = 88 which is also wrong, did i miss something agian?

4. Oct 1, 2005

### Tide

Yes, you did. The error from the xy term, for example, is $\delta x y = \delta x \times y + x \times \delta y$.

5. Oct 1, 2005

### Whatupdoc

i see that your using the product rule, but since 'y'and 2 is constant, cant you just take them out and just take the derivative of 'x'?

6. Oct 1, 2005

### Tide

Each of the 3 dimensions is, in fact, constant. The point is that there are errors in each of the 3 measurements and you can't selectively ignore any one of them in your error analysis.