# Thread: Differentials to estimate the maximum error

1. ## Differentials to estimate the maximum error

hey guys, i really don't know where to start where to end. plz help me solve this problem

The dimensions of a closed rectangular box are measured as 100 centimeters, 80 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.

___________________ square centimeters

2. Originally Posted by DMDil
hey guys, i really don't know where to start where to end. plz help me solve this problem

The dimensions of a closed rectangular box are measured as 100 centimeters, 80 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.

___________________ square centimeters
the surface area of the box is $S=2xy + 2yz + 2zx.$ thus $dS=2(y+z)dx + 2(x+z)dy + 2(x+y)dz.$ so: the maximum error in calculating $S \approx 0.2 \times (360 + 400 + 360) =224 \ \text{cm}^2$