Geometry/Math

Two right circular cylinders have equal volume. The first cylinder has a radius of 6 inches and a height of 12 inches. What is the number of inches in the height of the second cylinder if its radius is 8 inches? Express your answer as a common fraction, without units.

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1. volume of 1st = π(36)(12) = 432π

volume of 2nd = π(64)h

64π h = 432π
h = 432π/(64π)
= 27/4

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2. 27/4

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3. Stop Cheating! We have message boards for a reason. :D sike

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4. Yes, please DO NOT cheat use the message board if you are in trouble or needing assistance.

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5. Ya Boi!

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6. Called Out!

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7. Cheater cheater pumpkin eater friend me 9n Xbox my name is pcps
Aries

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9. Don’t cheat but make sure you understand the solution before moving on :D

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10. You can let him on it. Just maybe give some simple hints. Thank you!

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11. Do not misrepresent the work of others as your own
Do not take credit for the work of others and do not present the words or ideas of another person without properly giving credit.

It is supposed to be hard
The homework in AoPS classes requires complex and difficult thought. It requires creativity. Students need to struggle with deep and difficult problems in order to learn most effectively. When you take a shortcut through this process, you learn less.

Ask yourself: Why am I here? To become a math rockstar? To be the best I can be? To learn? If you are unwilling to struggle with problems, if you are unwilling to welcome adversity and challenge, your goals will always remain just goals, forever out of reach.

Collaborating with classmates
Work with other students! We very strongly believe that communication is an essential aspect of mathematics and working together is a great way to develop communication skills. However, you also need to understand the problem and participate meaningfully in the process in order to learn. When another student tells you the solution to a problem, that is not collaboration. When you watch another student solve a problem, that is not collaboration.

The solution that you submit should be your own solution in your own words. If you copy another student's solution into your assignment, this is misrepresenting another person's work as your own. If you are reading another student's solution as you create your assignment, this is misrepresenting another person's work as your own.

Use of the internet
You should not search for potential solutions to problems online or elsewhere. (Especially searching for the problem statement!) Using the internet in this way to search for answers is against our Course Policies! Instead, if you need some assistance with a particular problem, we welcome you to ask questions on your course message board. Your instructor and other AoPS staff members will be happy to help.

Again, the solution that you submit should be your own solution in your own words. If you copy a solution from the internet into your submission, this is misrepresenting another person's work as your own. If you are reading a solution from the internet as you create your submission, this is misrepresenting another person's work as your own.

Working with parents and tutors
Sometimes you need help and you have someone available.

Again, the solution that you submit should be your own solution in your own words. If you copy a solution from a friend, parent, or tutor into your submission, this is misrepresenting another person's work as your own. If you are reading a solution from a friend, parent, or tutor as you create your submission, this is misrepresenting another person's work as your own.

Give credit
When you do collaborate on your assignment or find an outside reference, be sure to cite your source. "My mom helped me with the second part," is a fine citation. "I worked in the classroom with Cuddlebug and ninjacat77" is as well.

Use the class Message Board
Don't forget that you can ask questions on the course message board. Posts you make on the class message board are forwarded to multiple class instructors who are happy to help. Use this resource!​ Hey (guess what?), you should use this resource.

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12. This is 100% correct!

1. 👍
2. 👎
13. Do not misrepresent the work of others as your own
Do not take credit for the work of others and do not present the words or ideas of another person without properly giving credit.

It is supposed to be hard
The homework in AoPS classes requires complex and difficult thought. It requires creativity. Students need to struggle with deep and difficult problems in order to learn most effectively. When you take a shortcut through this process, you learn less.

Ask yourself: Why am I here? To become a math rockstar? To be the best I can be? To learn? If you are unwilling to struggle with problems, if you are unwilling to welcome adversity and challenge, your goals will always remain just goals, forever out of reach.

Collaborating with classmates
Work with other students! We very strongly believe that communication is an essential aspect of mathematics and working together is a great way to develop communication skills. However, you also need to understand the problem and participate meaningfully in the process in order to learn. When another student tells you the solution to a problem, that is not collaboration. When you watch another student solve a problem, that is not collaboration.

The solution that you submit should be your own solution in your own words. If you copy another student's solution into your assignment, this is misrepresenting another person's work as your own. If you are reading another student's solution as you create your assignment, this is misrepresenting another person's work as your own.

Use of the internet
You should not search for potential solutions to problems online or elsewhere. (Especially searching for the problem statement!) Using the internet in this way to search for answers is against our Course Policies! Instead, if you need some assistance with a particular problem, we welcome you to ask questions on your course message board. Your instructor and other AoPS staff members will be happy to help.

Again, the solution that you submit should be your own solution in your own words. If you copy a solution from the internet into your submission, this is misrepresenting another person's work as your own. If you are reading a solution from the internet as you create your submission, this is misrepresenting another person's work as your own.

Working with parents and tutors
Sometimes you need help and you have someone available.

Again, the solution that you submit should be your own solution in your own words. If you copy a solution from a friend, parent, or tutor into your submission, this is misrepresenting another person's work as your own. If you are reading a solution from a friend, parent, or tutor as you create your submission, this is misrepresenting another person's work as your own.

Give credit
When you do collaborate on your assignment or find an outside reference, be sure to cite your source. "My mom helped me with the second part," is a fine citation. "I worked in the classroom with Cuddlebug and ninjacat77" is as well.

Use the class Message Board
Don't forget that you can ask questions on the course message board. Posts you make on the class message board are forwarded to multiple class instructors who are happy to help. Use this resource!​ Hey (guess what?), you should use this resource.

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