Trigonometry help.

[Braznor]

Hi,

I work in the IT department of a company full of engineers, but I'm not an engineer myself. I'm currently employed in the company as a consultant for SAP ERP currently used by my organization. Since I joined this company, I have developed an interest in learning mathematics and science (as a hobby, not for work). Right now I'm learning trigonometry using Michael Corral Trigonometry textbook. One of the exercises in the book stumps me very much and I have been hunting for a solution to it.

The book exercise says r = 0.944 in the solutions section. However I'm not getting how to derive the same. Here is the exercise as described in the text book :



1.3.25 A manufacturer needs to place ten identical ball bearings against the inner side of a circular container such that each ball bearing touches two other ball bearings, as in the picture on the right. The (inner) radius of the container is 44 cm.



(a) Find the common radius r of the ball bearings.
(b) The manufacturer needs to place a circular ring\\inside the container. What is the largest possible (outer) radius of the ring such that it is not on top\\of the ball bearings and its base is level with the\\base of the container?

I know this is elementary and basic. But it has been long since I have practiced mathematics since school and college. By the way, I'm 43 years old and I'm ashamed of being a maths brainlet. Please be assured this is not my school homework or anything.

Please help.

 

[sdifox]

Decagon with each of the point being the center of each circle.

 

[snoopy7548]

As an engineer, I find the best way to solve problems like this is to look at the answers in the back of the book.

 

[sdifox]

As an engineer, I find the best way to solve problems like this is to look at the answers in the back of the book.

Do you even google? I had to look up the name of a ten sided polygon even know I know it is supposed to be deca for ten and gon lol

 

[Braznor]

Please help!

The problem is eating my head......

 

[snoopy7548]

I never enjoyed trigonometry.

 

[sdifox]

Please help!

The problem is eating my head......

wtf, I already gave you a hint. you should be able to figure it out from there. Trig questions are about perspective more than anything else.

 

[SKORPI0]

Circle Packing -- from Wolfram MathWorld

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres is called a sphere packing. Tessellations of regular polygons correspond to particular circle packings (Williams 1979, pp...

mathworld.wolfram.com

Smaller Circles within a Large Circle - Calculator

Calculate the number of small circles that fits into an outer larger circle - ex. how many pipes or wires fits into a larger pipe or conduit.

www.engineeringtoolbox.com

 

[deadlyapp]

Hi,

I work in the IT department of a company full of engineers, but I'm not an engineer myself. I'm currently employed in the company as a consultant for SAP ERP currently used by my organization. Since I joined this company, I have developed an interest in learning mathematics and science (as a hobby, not for work). Right now I'm learning trigonometry using Michael Corral Trigonometry textbook. One of the exercises in the book stumps me very much and I have been hunting for a solution to it.

The book exercise says r = 0.944 in the solutions section. However I'm not getting how to derive the same. Here is the exercise as described in the text book :

View attachment 31986

1.3.25 A manufacturer needs to place ten identical ball bearings against the inner side of a circular container such that each ball bearing touches two other ball bearings, as in the picture on the right. The (inner) radius of the container is 44 cm.



(a) Find the common radius r of the ball bearings.
(b) The manufacturer needs to place a circular ring\\inside the container. What is the largest possible (outer) radius of the ring such that it is not on top\\of the ball bearings and its base is level with the\\base of the container?

I know this is elementary and basic. But it has been long since I have practiced mathematics since school and college. By the way, I'm 43 years old and I'm ashamed of being a maths brainlet. Please be assured this is not my school homework or anything.

Please help.

I think someone already posted some details, but you need to think about the circle that is inscribed by the center of all the bearings. The radius of that smaller circle is 4-r and the circumference of that circle can be derived through that and the known outer circumference of the outer race.

 

[IronWing]

Place ten balls known to be too large in the bearing . They will grind themselves down to the correct size. Once the bearing stops making noise, measure the balls.

 

[dullard]

 

[Fritzo]

 

[snoopy7548]

View attachment 32000

Are you a wizard or something?

 

[Braznor]

View attachment 32000

Thank you, Thank You, Thank You.

Atlast I can get a good sleep and some peace of mind.

 

[Braznor]

wtf, I already gave you a hint. you should be able to figure it out from there. Trig questions are about perspective more than anything else.

Thank You,

I'm trying to work it out your way.

 

[BarkingGhostar]

As an engineer, I find the best way to solve problems like this is to look at the answers in the back of the book.

You jackass! That's the difference between those that can and those that do. Dullard has the answer, which I got immediately, but that's another story. Look at the answers in the back of the book ...

 

[snoopy7548]

You jackass! That's the difference between those that can and those that do. Dullard has the answer, which I got immediately, but that's another story. Look at the answers in the back of the book ...

At least I'm not the management type (those that can't)... just get others to do it for you!

But I hear it pays pretty well...

 

[SKORPI0]

View attachment 32000

So you just had to spoon feed the OP by posting how to solve it.

 

[dullard]

So you just had to spoon feed the OP by posting how to solve it.

Best way to learn: struggle then have someone show you the way.

 

[BarkingGhostar]

At least I'm not the management type (those that can't)... just get others to do it for you!

But I hear it pays pretty well...

A manager I had twenty years ago said, "I don't need to know how to do it (meaning my job), as his job was to manage those that did know." As he said this I remembered this guy from an ATM class teaching us about Asynchronous Mode Transport and telling us about the smoke and mirrors we would get into later--he was talking about virtual circuits in ATM. But I beg to differ on your front. As an engineer it should be automatic to solve the problem by not going to the other guy (who wrote the answer in a book) unless it is standard/reference data. That problem wasn't hard, just cluttered to make it look hard.

 

[Spacehead]

About 15-20 years ago the boss got pissed at me for using one of the computers to figure out some roll dimension for work. So since then i'll sit at my bench & figure stuff with pencil & paper & sometimes take way longer than just going & using software.
I do like being able to figure things on my own but there are some things i just haven't found formulas for & i need to have someone figure for me on the computer. I've never used AutoCad so someone else has to do it for me.