Answer:
the maximum error in calculating the surface area of the box is 152 cm2
Explanation:
Assuming he dimensions of the box is l, w and h (for length, width and height). The surface area is then: S(l, w, h) = 2lw + 2wh + 2lh = 2(lw + wh + lh)
The change in area can be written as: ∆S ≈ dS = Sl dl + Sw dw + Sh dh
where the partial derivatives are evaluated at l = 80, w = 60 and h = 50, and
dl = dw = dh = 0.2.
The partial derivatives are computed:
Sl = 2(w + h) = 220 Sw = 2(l + h) = 260 Sh = 2(l + w) = 280
Substituting these in for dS,
dS = 220 · 0.2 + 260 · 0.2 + 280 · 0.2 = 152 cm2
