Answer:
The maximum error in calculating the surface area of the box is 152 square cm.
Step-by-step explanation:
We are given the following information in the question:
The dimensions of a closed rectangular box are measured as 80 cm, 60 cm, 50 cm, respectively.
Possible error = 0.2 cm
Surface area of rectangular box =
[tex]S = 2(lb + bh + lh)[/tex]
where l, b and h are the length, breadth and height of the rectangular box respectively.
Change in area =
[tex]\Delta S \approx dS = 2(l\Delta b + b\Delta l + b\Delta h + h\Delta b + l\Delta h + h\Delta l)\\[/tex]
Putting the values, we get,
Change in area =
[tex]=2(\Delta l (b+h) + \Delta b (h+l) + \Deltah(l + b))\\=2(0.2(110) + 0.2(130) + 0.2(140))\\= 152\text{ square cm}[/tex]
The maximum error in calculating the surface area of the box is 152 square cm.
