The dimensions of a closed rectangular box are measured as 96 cm, 58 cm, and 48 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.

Step-by-step explanation:

Surface Area of the rectangular box = 2(LW+LH+WH)

L is the length of the box

W is the width of the box

H is the height of the box

let dL, dW and dH be the possible error in the dimensions L, W and H respectively.

Since there is a possible error of 0.2cm in each dimension, then dL = dW = dH = 0.2cm

The surface Area of the rectangular box using the differentials is expressed as shown;

S = 2{(LdW+WdL)+(LdH+HdL)+(WdH+HdW)]

Also given L = 96cm W = 58cm and H = 48cm, on substituting this given values and the differential error, we will have;

S = 2{(96*0.2+58*0.2) + (96*0.2+48*0.2)+(58*0.2+48*0.2)}

S = 2{19.2+11.6+19.2+9.6+11.6+9.6}

S = 2(80.8)

S = 161.6 cm²

Hence, the surface area of the box is 161.6 cm²