Check work on finding max error of Surface Area

[tnutty]

Homework Statement

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

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

which is about 0.06% error.

Is this correct?

 

[Mark44]

Homework Statement

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

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

which is about 0.06% error.

Is this correct?

That's what I get.

 

[tnutty]

Thanks

 

[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.

 

[Mark44]

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.

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

 

[blake knight]

Is your answer 0.06% derived from 152/23600?

 

[03125]

0.2((2y+2z)+(2x+2z)+(2y+2x))

where
(2y+2z) is the partial derivative of SA with respect to x
(2x+2z) is the partial derivative of SA with respect to y
(2y+2x) is the partial derivative of SA with respect to z