Solids of Revolution [on hold]
Given a function f, if we rotate its graph around the x-axis we can construct an expression for the volume of the resulting solid approximating it by a bunch of cylinders (and using integration as the number of cylinders goes to infinity). I was wondering if we get to the same result if we use cones instead of cylinders on the approximation for the volume.
calculus integration solid-of-revolution
asked 2 days ago
user596283
1
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put on hold as off-topic by Eevee Trainer, Leucippus, Lord_Farin, Cesareo, user91500 yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
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Given a function f, if we rotate its graph around the x-axis we can construct an expression for the volume of the resulting solid approximating it by a bunch of cylinders (and using integration as the number of cylinders goes to infinity). I was wondering if we get to the same result if we use cones instead of cylinders on the approximation for the volume.
calculus integration solid-of-revolution
asked 2 days ago
user596283
1
New contributor
user596283 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, Leucippus, Lord_Farin, Cesareo, user91500 yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Leucippus, Lord_Farin, Cesareo, user91500
If this question can be reworded to fit the rules in the help center, please edit the question.
The cones generally won't fit the specified curves.
– David G. Stork
2 days ago
Try doing the math.
– Henrik
2 days ago
add a comment |
Given a function f, if we rotate its graph around the x-axis we can construct an expression for the volume of the resulting solid approximating it by a bunch of cylinders (and using integration as the number of cylinders goes to infinity). I was wondering if we get to the same result if we use cones instead of cylinders on the approximation for the volume.
calculus integration solid-of-revolution
asked 2 days ago
user596283
1
New contributor
user596283 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Given a function f, if we rotate its graph around the x-axis we can construct an expression for the volume of the resulting solid approximating it by a bunch of cylinders (and using integration as the number of cylinders goes to infinity). I was wondering if we get to the same result if we use cones instead of cylinders on the approximation for the volume.
calculus integration solid-of-revolution
calculus integration solid-of-revolution
asked 2 days ago
user596283
1
New contributor
user596283 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
user596283
1
New contributor
user596283 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
user596283
1
New contributor
user596283 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
user596283
1
asked 2 days ago
user596283
1
1
New contributor
user596283 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user596283 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user596283 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, Leucippus, Lord_Farin, Cesareo, user91500 yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Leucippus, Lord_Farin, Cesareo, user91500
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Eevee Trainer, Leucippus, Lord_Farin, Cesareo, user91500 yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Leucippus, Lord_Farin, Cesareo, user91500
If this question can be reworded to fit the rules in the help center, please edit the question.
The cones generally won't fit the specified curves.
– David G. Stork
2 days ago
Try doing the math.
– Henrik
2 days ago
add a comment |
The cones generally won't fit the specified curves.
– David G. Stork
2 days ago
Try doing the math.
– Henrik
2 days ago
The cones generally won't fit the specified curves.
– David G. Stork
2 days ago
The cones generally won't fit the specified curves.
– David G. Stork
2 days ago
Try doing the math.
– Henrik
2 days ago
Try doing the math.
– Henrik
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
I think we can use the fact that a cone with the same base area and height as a cylinder has $frac{1}{3}$ the volume of the cylinder.
$$V_{cone}=frac{pi r^2h}{3}$$
$$V_{cylinder}=pi r^2h$$
answered 2 days ago
Larry
1,6082722
This is true but as the numbers of cones and cylinders goes to infinity shouldn't we get the same value for the solid's volume?
– user596283
2 days ago
Although the thickness is infinitely small, the volume of a cone is still one third of that of a cylinder. It does not really matter how many there are.
– Larry
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
I think we can use the fact that a cone with the same base area and height as a cylinder has $frac{1}{3}$ the volume of the cylinder.
$$V_{cone}=frac{pi r^2h}{3}$$
$$V_{cylinder}=pi r^2h$$
answered 2 days ago
Larry
1,6082722
This is true but as the numbers of cones and cylinders goes to infinity shouldn't we get the same value for the solid's volume?
– user596283
2 days ago
Although the thickness is infinitely small, the volume of a cone is still one third of that of a cylinder. It does not really matter how many there are.
– Larry
2 days ago
add a comment |
I think we can use the fact that a cone with the same base area and height as a cylinder has $frac{1}{3}$ the volume of the cylinder.
$$V_{cone}=frac{pi r^2h}{3}$$
$$V_{cylinder}=pi r^2h$$
answered 2 days ago
Larry
1,6082722
This is true but as the numbers of cones and cylinders goes to infinity shouldn't we get the same value for the solid's volume?
– user596283
2 days ago
Although the thickness is infinitely small, the volume of a cone is still one third of that of a cylinder. It does not really matter how many there are.
– Larry
2 days ago
add a comment |
I think we can use the fact that a cone with the same base area and height as a cylinder has $frac{1}{3}$ the volume of the cylinder.
$$V_{cone}=frac{pi r^2h}{3}$$
$$V_{cylinder}=pi r^2h$$
answered 2 days ago
Larry
1,6082722
I think we can use the fact that a cone with the same base area and height as a cylinder has $frac{1}{3}$ the volume of the cylinder.
$$V_{cone}=frac{pi r^2h}{3}$$
$$V_{cylinder}=pi r^2h$$
answered 2 days ago
Larry
1,6082722
answered 2 days ago
Larry
1,6082722
answered 2 days ago
Larry
1,6082722
answered 2 days ago
Larry
1,6082722
1,6082722
This is true but as the numbers of cones and cylinders goes to infinity shouldn't we get the same value for the solid's volume?
– user596283
2 days ago
Although the thickness is infinitely small, the volume of a cone is still one third of that of a cylinder. It does not really matter how many there are.
– Larry
2 days ago
add a comment |
This is true but as the numbers of cones and cylinders goes to infinity shouldn't we get the same value for the solid's volume?
– user596283
2 days ago
Although the thickness is infinitely small, the volume of a cone is still one third of that of a cylinder. It does not really matter how many there are.
– Larry
2 days ago
This is true but as the numbers of cones and cylinders goes to infinity shouldn't we get the same value for the solid's volume?
– user596283
2 days ago
This is true but as the numbers of cones and cylinders goes to infinity shouldn't we get the same value for the solid's volume?
– user596283
2 days ago
Although the thickness is infinitely small, the volume of a cone is still one third of that of a cylinder. It does not really matter how many there are.
– Larry
2 days ago
Although the thickness is infinitely small, the volume of a cone is still one third of that of a cylinder. It does not really matter how many there are.
– Larry
2 days ago
add a comment |
The cones generally won't fit the specified curves.
– David G. Stork
2 days ago
Try doing the math.
– Henrik
2 days ago