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xz_007 [3.2K]
3 years ago
14

A worker is cutting a square from a piece of sheet metal. The specifications call for an area that is 16 cm squared with an erro

r of no more than 0.03 cm squared. How much error could be tolerated in the length of each side to ensure that the area is within the​ tolerance?
Mathematics
1 answer:
masha68 [24]3 years ago
3 0

Given:

area of square, A = 16 cm^{2}

error in area, dA = 0.03 cm^{2}

Step-by-Step Explanation:

Let 'a' be the side of the square

area of square, A = a^{2}                 (1)

A = 16 =  a^{2}

Therefore, a = 4 cm

for max tolerable error in length 'da', differentiate eqn (1) w.r.t 'a':

dA = 2a da

0.03 = 2\times 4\times da

da = \frac{0.03}{8}

da = 0.0375 cm

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