The dimensions of a closed rectangular box are measured as 9

Solution

Let l-length of the box-94cm

     b- width of the box=57cm

   h - height of the box=26cm

   error in measurement of each dimension-0.2cm

the surface area of the box is:
S = 2(lb+bh+hl)

By differentiating:
dS = [2b(dl) + 2l(db)] + [2h(dl) + 2l(dh)] + [2h(db) + 2b(dl)]
= (2b + 2h)(dl) + (2l + 2h)(db) + (2l + 2b)(dh).

Since dl = db = dh = 0.2,l = 94, b = 57, and h = 26
dS = (114 + 52)(0.2) + (188+ 52)(0.2) + (188+ 114)(0.2)
= 141.6cm²

Thus, the maximum error in calculating the surface area of the box is 141.6 cm²