Help! Finding a set of percentages based on bisecting a cylinder?

[agibberjabber]

I am helping a friend out by asking this question. I would love to know what equation is needed plus the answer, if possible. This is not for schoolwork but is needed for functional application. Here is the problem:

You have a shallow solid cylinder made of organic material. The diameter of the cylinder is 1/4 of 1". You align the cylinder with a ruler which has lines at every 1/32 of an inch, so the cylinder can be cut with 7 straight parallel lines across the diameter to create 8 sections, using these lines to determine the distance between cuts. You make 4 cuts inward toward the center of the cylinder using the lines on the ruler. At your fourth cut, what is remaining of the cylinder will be exactly half, 50% of the original cylinder, and exactly 50% will have been removed. The question is: What percentage of the cylinder was removed with the 1st, 2nd, and 3rd cuts? The 1st cut went 1/8 of the distance of the diameter into the cylinder just like the other cuts do, but because the cut is being made across the edge of the cylinder, this "piece" has less mass than the 2nd, 3rd, and 4th cuts. How do I determine the percentage of the whole that is removed with each cut?

Looking forward to helping a friend and wondering how the answers are reached. Thanks so much!

 

[Dr.Peterson]

I am helping a friend out by asking this question. I would love to know what equation is needed plus the answer, if possible. This is not for schoolwork but is needed for functional application. Here is the problem:

You have a shallow solid cylinder made of organic material. The diameter of the cylinder is 1/4 of 1". You align the cylinder with a ruler which has lines at every 1/32 of an inch, so the cylinder can be cut with 7 straight parallel lines across the diameter to create 8 sections, using these lines to determine the distance between cuts. You make 4 cuts inward toward the center of the cylinder using the lines on the ruler. At your fourth cut, what is remaining of the cylinder will be exactly half, 50% of the original cylinder, and exactly 50% will have been removed. The question is: What percentage of the cylinder was removed with the 1st, 2nd, and 3rd cuts? The 1st cut went 1/8 of the distance of the diameter into the cylinder just like the other cuts do, but because the cut is being made across the edge of the cylinder, this "piece" has less mass than the 2nd, 3rd, and 4th cuts. How do I determine the percentage of the whole that is removed with each cut?

Looking forward to helping a friend and wondering how the answers are reached. Thanks so much!

Any of these cuts makes a segment of a circle; you can see a formula for the area here. The area of each piece between cuts can be found by subtracting the areas of successive segments.

See if you can work out what you want from that.

 

[Deleted member 4993]

I am helping a friend out by asking this question. I would love to know what equation is needed plus the answer, if possible. This is not for schoolwork but is needed for functional application. Here is the problem:

You have a shallow solid cylinder made of organic material. The diameter of the cylinder is 1/4 of 1". You align the cylinder with a ruler which has lines at every 1/32 of an inch, so the cylinder can be cut with 7 straight parallel lines across the diameter to create 8 sections, using these lines to determine the distance between cuts. You make 4 cuts inward toward the center of the cylinder using the lines on the ruler. At your fourth cut, what is remaining of the cylinder will be exactly half, 50% of the original cylinder, and exactly 50% will have been removed. The question is: What percentage of the cylinder was removed with the 1st, 2nd, and 3rd cuts? The 1st cut went 1/8 of the distance of the diameter into the cylinder just like the other cuts do, but because the cut is being made across the edge of the cylinder, this "piece" has less mass than the 2nd, 3rd, and 4th cuts. How do I determine the percentage of the whole that is removed with each cut?

Looking forward to helping a friend and wondering how the answers are reached. Thanks so much!

Since this is an application problem - there is a practical solution.

First you need a good and accurate weighing machine (more precise/accurate than ordinary kitchen balance)

Get a thick uniform piece of thick cardboard - ~16" x 16"

Draw a circle of radius 6" (Dia 12") - and cut it out carefully.

Now weigh the circular cut-out.

Now you can cutout the slices - weigh those - and calculate percentages.

 

[agibberjabber]

Thanks!

Thank you! Would love to have done it the practical way cause it sounds like fun, but the calculator worked great! Thanks for all your help!