Volume of a hollow cylinder
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Volumen \(V\) / Höhe \(h\) / Radius \(r\) /
The following formulas must be used to solve the exercise:
\(V = \pi h (R^2-r^2) \quad \)
No explanation / solution video to this exercise has yet been created.
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Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
abcliste abc A copper pipe has araO outer radius and ariO inner radius. How much copper by volume was the alO long pipe made from? One inch is .cm one foot is .cm. abc A copper pipe has an inner radius of briO and is blO long. The volume of copper used is bVO. What is the outer radius of the pipe? abc A copper pipe has an outer radius of craO and is clO long. The volume of copper used is cVO. What is the inner radius of the pipe? abc A copper pipe has an outer radius of draO and an inner radius of driO. The volume of copper used is dVO. How long is the pipe? abcliste
Solution:
abcliste abc V pi R^-r^ h pi r_^-r_^ h pi leftqtyara^-qtyari^right al aV approx aVS abc R sqrtfracVpi h+r^ sqrtfracbVpi bl+bri^ bra approx braS abc r sqrtR^-fracVpi h sqrtcra^-fraccVpi cl cri approx criS abc h fracVpiR^-r^ fracdVpidra^-dri^ dl approx dlS abcliste
abcliste abc A copper pipe has araO outer radius and ariO inner radius. How much copper by volume was the alO long pipe made from? One inch is .cm one foot is .cm. abc A copper pipe has an inner radius of briO and is blO long. The volume of copper used is bVO. What is the outer radius of the pipe? abc A copper pipe has an outer radius of craO and is clO long. The volume of copper used is cVO. What is the inner radius of the pipe? abc A copper pipe has an outer radius of draO and an inner radius of driO. The volume of copper used is dVO. How long is the pipe? abcliste
Solution:
abcliste abc V pi R^-r^ h pi r_^-r_^ h pi leftqtyara^-qtyari^right al aV approx aVS abc R sqrtfracVpi h+r^ sqrtfracbVpi bl+bri^ bra approx braS abc r sqrtR^-fracVpi h sqrtcra^-fraccVpi cl cri approx criS abc h fracVpiR^-r^ fracdVpidra^-dri^ dl approx dlS abcliste
Meta Information
Exercise:
abcliste abc A copper pipe has araO outer radius and ariO inner radius. How much copper by volume was the alO long pipe made from? One inch is .cm one foot is .cm. abc A copper pipe has an inner radius of briO and is blO long. The volume of copper used is bVO. What is the outer radius of the pipe? abc A copper pipe has an outer radius of craO and is clO long. The volume of copper used is cVO. What is the inner radius of the pipe? abc A copper pipe has an outer radius of draO and an inner radius of driO. The volume of copper used is dVO. How long is the pipe? abcliste
Solution:
abcliste abc V pi R^-r^ h pi r_^-r_^ h pi leftqtyara^-qtyari^right al aV approx aVS abc R sqrtfracVpi h+r^ sqrtfracbVpi bl+bri^ bra approx braS abc r sqrtR^-fracVpi h sqrtcra^-fraccVpi cl cri approx criS abc h fracVpiR^-r^ fracdVpidra^-dri^ dl approx dlS abcliste
abcliste abc A copper pipe has araO outer radius and ariO inner radius. How much copper by volume was the alO long pipe made from? One inch is .cm one foot is .cm. abc A copper pipe has an inner radius of briO and is blO long. The volume of copper used is bVO. What is the outer radius of the pipe? abc A copper pipe has an outer radius of craO and is clO long. The volume of copper used is cVO. What is the inner radius of the pipe? abc A copper pipe has an outer radius of draO and an inner radius of driO. The volume of copper used is dVO. How long is the pipe? abcliste
Solution:
abcliste abc V pi R^-r^ h pi r_^-r_^ h pi leftqtyara^-qtyari^right al aV approx aVS abc R sqrtfracVpi h+r^ sqrtfracbVpi bl+bri^ bra approx braS abc r sqrtR^-fracVpi h sqrtcra^-fraccVpi cl cri approx criS abc h fracVpiR^-r^ fracdVpidra^-dri^ dl approx dlS abcliste
Contained in these collections:
-
Hohlzylindervolumen by TeXercises
-
Volumen by uz
Asked Quantity:
Volumen \(V\)
in
Kubikmeter \(\rm m^3\)
Physical Quantity
Rauminhalt
Unit
Kubikmeter (\(\rm m^3\))
Base?
SI?
Metric?
Coherent?
Imperial?

