Mathematics: The dimensions of a closed rectangular box are measured as80cm, 60 cm, 50cm, respectively, with a possible error of .2 cm ineach dimension. use differentials to estimate the maximumerror in calculating the surface area of the box.

132Step-by-step explanation:gnh=3 knl×2=100 mnl=1...

The dimensions of a closed rectangular box are measured

lorelaistudent

14.01.2022

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 =

S = 2(lb + bh + lh)

where l, b and h are the length, breadth and height of the rectangular box respectively.

Change in area =

$\Delta S \approx dS = 2(l\Delta b + b\Delta l + b\Delta h + h\Delta b + l\Delta h + h\Delta l)\\$

Putting the values, we get,

Change in area =

$=2(\Delta l (b+h) + \Delta b (h+l) + \Deltah(l + b))\\=2(0.2(110) + 0.2(130) + 0.2(140))\\= 152\text{ square cm}$

The maximum error in calculating the surface area of the box is 152 square cm.

0,0(0 оценок)