The volume of the cube is claimed to be 27 inches, correct to within 0.027 i n 3

Fescoisyncsibgyp8b

Fescoisyncsibgyp8b

Answered question

2022-05-14

The volume of the cube is claimed to be 27 inches, correct to within 0.027 i n 3 . Use differentials to estimate the propagated error in the measurement of the side of the cube.
I got
V = 27
v = x 3 , which x=3 inches
d V = 3 x 2 d x
0.027 = 27 d x
dx=+2 and −2
But I am not sure what the answer of this question is.

Answer & Explanation

glapaso7ng5

glapaso7ng5

Beginner2022-05-15Added 13 answers

You are correct that
d V = 3 x 2 d x
For the interpretation, d V is the error in volume, x is the side of the cube, and d x is the error in the side of the cube. Substituting, we get
0.027 = 3 ( 3 ) 2 d x
d x = 0.027 3 9
= 0.001

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