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liberstina [14]
3 years ago
14

The dimensions of a closed rectangular box are measured as 50 centimeters, 60 centimeters, and 70 centimeters, respectively, wit

h the error in each measurement at most .2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.
Social Studies
1 answer:
Inessa [10]3 years ago
8 0

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

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