SOLUTION: The volume of the rectangular block in the figure is calculated from the following measurements of its dimensions: 𝑎=10.00±0.10 cm, 𝑏=5.00±0.06 cm and 𝑐=4.00±0.04 cm

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Question 1181820: The volume of the rectangular block in the figure is calculated from the following measurements of its dimensions:
𝑎=10.00±0.10 cm, 𝑏=5.00±0.06 cm and 𝑐=4.00±0.04 cm.
Calculate the error in the value of the volume of the block assuming:
a) the errors are independent
b) the errors are correlated such that they all push the estimate in the same direction.
Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
If , then
a)
= 5*4*(±0.10) + 10*4*(±0.06) + 10*5*(±0.04)
= ±2 ±2.4 ±2 = ± 6.4
b) Either 6.4 when all variables are increasing, or -6.4, when all variables are decreasing.
Answer by ikleyn(52900)   (Show Source): You can put this solution on YOUR website!
.

With the given margins of measurements, the upper bound of the calculated volume is


     = (10 + 0.1)*(5 + 0.06)*(4 + 0.04) = 206.46824  cm^3,

or   -  = 6.46824 cm^3  more than the "precise" value of the volume V = 10*5*4 = 200 cm^3.




With the given margins of measurements, the lower bound of the calculated volume is


     = (10 - 0.1)*(5 - 0.06)*(4 - 0.04) = 193.66776  cm^3,

or   -  = 6.33224 cm^3  less than the "precise" value of the volume V = 10*5*4 = 200 cm^3.



So, you can write THIS INEQUALITY


     = 193.66776 = 200-6.33224 <= V <= 206.46824 =  = V + 6.46824  cubic centimeters


and this inequality COVERS BOTH questions in your post.


Solved, answered and explained.



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