# Homework Help: Check work on finding max error of Surface Area

1. Oct 18, 2009

### tnutty

1. The problem statement, all variables and given/known data
The dimensions of a closed rectangular box are measured as 80cm, 60cm, and 50cm,respectively,
with a possible error of 0.2cm in each dimension. Use differentials to estimate the maximum error
in calculating the surface area of the box

3. The attempt at a solution

I figured out that the surface area of a closed rectangular box is this :

SA = 2[ xy + yz + xz]

so, differentiating with respect to x,y and z I get :

d[SA] = 2[ yzD_x + xzD_y + xyD_y]

inserting value,
x = 80
y = 60
z = 50
dx = dy = dz = 0.2 ; since this is where the max error will occur I get

d[SA] = 152cm^2

Is this correct?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 18, 2009

### Staff: Mentor

That's what I get.

3. Oct 18, 2009

### tnutty

Thanks

4. Oct 18, 2009

### Black Jackal

Ummm...i plugged in The numbers for this, and my answer is too big (4720) when x=80,y=60,z=50, and the d's being 0.2 exactly how were the numbers plugged in? There is a step i'm missing.

5. Oct 19, 2009

### Staff: Mentor

What formula did you use? Both the OP and I got exactly the same result with the formula he posted.

6. Oct 19, 2009