Error in cross sectional area of a cylinder, given circumference is $8$ feet $pm 1$ inch
Given a cylinder with the circumference of $8$ feet $pm 1$ inch, how could the error in the cross sectional area be found?
As per request:
Given that the area of the cross section is a circle, $A=pi r^2$, and the circumference is just $C=2 pi r$. In terms of the area $pi (C/(2pi))^2$. I am not sure what to do after that. I know I have to use differentials but I'm not sure how to relate the two.
calculus area
edited Dec 1 at 10:25
Brahadeesh
6,11742360
asked Nov 30 at 16:56
ovil101
273
add a comment |
Given a cylinder with the circumference of $8$ feet $pm 1$ inch, how could the error in the cross sectional area be found?
As per request:
Given that the area of the cross section is a circle, $A=pi r^2$, and the circumference is just $C=2 pi r$. In terms of the area $pi (C/(2pi))^2$. I am not sure what to do after that. I know I have to use differentials but I'm not sure how to relate the two.
calculus area
edited Dec 1 at 10:25
Brahadeesh
6,11742360
asked Nov 30 at 16:56
ovil101
273
1
compute the cross sectional area with circumference 7 feet 11 inches and 8 feet 1 inch.
– Don Thousand
Nov 30 at 17:00
1
People tend to be more interested here in questions that show an effort to solve the problem, showing in detail what you did and where you got stuck so someone might help you past that specific difficulty. Please see math.stackexchange.com/help/how-to-ask
– David K
Nov 30 at 17:00
I have updated the post David
– ovil101
Nov 30 at 17:12
I think error propagation formula would be more efficient and meaningful rather than brute force calculation of limiting cases.
– ggcg
Nov 30 at 17:29
add a comment |
Given a cylinder with the circumference of $8$ feet $pm 1$ inch, how could the error in the cross sectional area be found?
As per request:
Given that the area of the cross section is a circle, $A=pi r^2$, and the circumference is just $C=2 pi r$. In terms of the area $pi (C/(2pi))^2$. I am not sure what to do after that. I know I have to use differentials but I'm not sure how to relate the two.
calculus area
edited Dec 1 at 10:25
Brahadeesh
6,11742360
asked Nov 30 at 16:56
ovil101
273
Given a cylinder with the circumference of $8$ feet $pm 1$ inch, how could the error in the cross sectional area be found?
As per request:
Given that the area of the cross section is a circle, $A=pi r^2$, and the circumference is just $C=2 pi r$. In terms of the area $pi (C/(2pi))^2$. I am not sure what to do after that. I know I have to use differentials but I'm not sure how to relate the two.
calculus area
calculus area
edited Dec 1 at 10:25
Brahadeesh
6,11742360
asked Nov 30 at 16:56
ovil101
273
edited Dec 1 at 10:25
Brahadeesh
6,11742360
asked Nov 30 at 16:56
ovil101
273
edited Dec 1 at 10:25
Brahadeesh
6,11742360
edited Dec 1 at 10:25
Brahadeesh
6,11742360
edited Dec 1 at 10:25
Brahadeesh
6,11742360
6,11742360
asked Nov 30 at 16:56
ovil101
273
asked Nov 30 at 16:56
ovil101
273
asked Nov 30 at 16:56
ovil101
273
273
1
compute the cross sectional area with circumference 7 feet 11 inches and 8 feet 1 inch.
– Don Thousand
Nov 30 at 17:00
1
People tend to be more interested here in questions that show an effort to solve the problem, showing in detail what you did and where you got stuck so someone might help you past that specific difficulty. Please see math.stackexchange.com/help/how-to-ask
– David K
Nov 30 at 17:00
I have updated the post David
– ovil101
Nov 30 at 17:12
I think error propagation formula would be more efficient and meaningful rather than brute force calculation of limiting cases.
– ggcg
Nov 30 at 17:29
add a comment |
1
compute the cross sectional area with circumference 7 feet 11 inches and 8 feet 1 inch.
– Don Thousand
Nov 30 at 17:00
1
People tend to be more interested here in questions that show an effort to solve the problem, showing in detail what you did and where you got stuck so someone might help you past that specific difficulty. Please see math.stackexchange.com/help/how-to-ask
– David K
Nov 30 at 17:00
I have updated the post David
– ovil101
Nov 30 at 17:12
I think error propagation formula would be more efficient and meaningful rather than brute force calculation of limiting cases.
– ggcg
Nov 30 at 17:29
1
1
compute the cross sectional area with circumference 7 feet 11 inches and 8 feet 1 inch.
– Don Thousand
Nov 30 at 17:00
compute the cross sectional area with circumference 7 feet 11 inches and 8 feet 1 inch.
– Don Thousand
Nov 30 at 17:00
1
1
People tend to be more interested here in questions that show an effort to solve the problem, showing in detail what you did and where you got stuck so someone might help you past that specific difficulty. Please see math.stackexchange.com/help/how-to-ask
– David K
Nov 30 at 17:00
People tend to be more interested here in questions that show an effort to solve the problem, showing in detail what you did and where you got stuck so someone might help you past that specific difficulty. Please see math.stackexchange.com/help/how-to-ask
– David K
Nov 30 at 17:00
I have updated the post David
– ovil101
Nov 30 at 17:12
I have updated the post David
– ovil101
Nov 30 at 17:12
I think error propagation formula would be more efficient and meaningful rather than brute force calculation of limiting cases.
– ggcg
Nov 30 at 17:29
I think error propagation formula would be more efficient and meaningful rather than brute force calculation of limiting cases.
– ggcg
Nov 30 at 17:29
add a comment |
1 Answer
1
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oldest
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Use Circumference=$2πr$ given that r is only data to be measured and, $2π$ are both constant.The uncertainty in r (∆r = 1 foot).
Now you can easily find uncertainty in Area since Area=$r^2$.
$$Percentage Uncertainty= frac{2∆r}{r} $$
$$ error=frac{PU}{100}.Area$$
Now you have the answer.
answered Nov 30 at 17:34
PiGuy
1487
add a comment |
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1 Answer
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votes
Use Circumference=$2πr$ given that r is only data to be measured and, $2π$ are both constant.The uncertainty in r (∆r = 1 foot).
Now you can easily find uncertainty in Area since Area=$r^2$.
$$Percentage Uncertainty= frac{2∆r}{r} $$
$$ error=frac{PU}{100}.Area$$
Now you have the answer.
answered Nov 30 at 17:34
PiGuy
1487
add a comment |
Use Circumference=$2πr$ given that r is only data to be measured and, $2π$ are both constant.The uncertainty in r (∆r = 1 foot).
Now you can easily find uncertainty in Area since Area=$r^2$.
$$Percentage Uncertainty= frac{2∆r}{r} $$
$$ error=frac{PU}{100}.Area$$
Now you have the answer.
answered Nov 30 at 17:34
PiGuy
1487
add a comment |
Use Circumference=$2πr$ given that r is only data to be measured and, $2π$ are both constant.The uncertainty in r (∆r = 1 foot).
Now you can easily find uncertainty in Area since Area=$r^2$.
$$Percentage Uncertainty= frac{2∆r}{r} $$
$$ error=frac{PU}{100}.Area$$
Now you have the answer.
answered Nov 30 at 17:34
PiGuy
1487
Use Circumference=$2πr$ given that r is only data to be measured and, $2π$ are both constant.The uncertainty in r (∆r = 1 foot).
Now you can easily find uncertainty in Area since Area=$r^2$.
$$Percentage Uncertainty= frac{2∆r}{r} $$
$$ error=frac{PU}{100}.Area$$
Now you have the answer.
answered Nov 30 at 17:34
PiGuy
1487
answered Nov 30 at 17:34
PiGuy
1487
answered Nov 30 at 17:34
PiGuy
1487
answered Nov 30 at 17:34
PiGuy
1487
1487
add a comment |
add a comment |
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1
compute the cross sectional area with circumference 7 feet 11 inches and 8 feet 1 inch.
– Don Thousand
Nov 30 at 17:00
1
People tend to be more interested here in questions that show an effort to solve the problem, showing in detail what you did and where you got stuck so someone might help you past that specific difficulty. Please see math.stackexchange.com/help/how-to-ask
– David K
Nov 30 at 17:00
I have updated the post David
– ovil101
Nov 30 at 17:12
I think error propagation formula would be more efficient and meaningful rather than brute force calculation of limiting cases.
– ggcg
Nov 30 at 17:29