The volume V of a cylinder is computed using the values 6m for the diameter and 9.8 m for

Reginald Delacruz

Reginald Delacruz

Answered question

2022-06-27

The volume V of a cylinder is computed using the values 6m for the diameter and 9.8m for the height. Use the linear approximation to estimate the maximum error in V if each of these values has a possible error of at most 7%.

Answer & Explanation

Belen Bentley

Belen Bentley

Beginner2022-06-28Added 28 answers

V = π r 2 h
d V = d V d r d r + d V d h d h
= ( 2 π r h ) d r + ( π r 2 ) d h
d V V = 2 ( d r / r ) + ( d h / h ) = 2 ( .07 ) + ( .07 ) = 0.21
Thus the relative error in V is 21 percent.
Boilanubjaini8f

Boilanubjaini8f

Beginner2022-06-29Added 6 answers

Volume of a cylinder V = π 4 d 2 h
Possible error in volume
= π 4 [ ( 1 ± 0.007 ) d ] 2 [ ( 1 ± 0.007 ) h ]
= π 4 [ ( 1 ± 0.007 ) 3 ] d 2 h
= v ( 1 ± 0.07 ) 3
Now the percentage error in = 1.225042 => + 22.5043

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