gold coin belt problem

irene12

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Dec 21, 2010
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I have an extra credit problem I can't begin to figure out. Any ideas? Thank you
Leia has enough gold coins to place them side by side and create a belt around the earth at the equator. Mike has more than enough coins to create a belt around the earth at least 2 cm above the equator. the coins are identical, with diameter 2 cm. What is the smallest number of coins by which mike 's hoard surpasses Leia's
 
irene12 said:
I have an extra credit problem I can't begin to figure out. Any ideas? Thank you
Leia has enough gold coins to place them side by side and create a belt around the earth at the equator. Mike has more than enough coins to create a belt around the earth at least 2 cm above the equator. the coins are identical, with diameter 2 cm. What is the smallest number of coins by which mike 's hoard surpasses Leia's

Did you make aan approximate sketch of the problem?

How much bigger (in centimeters) is Mike's belt?
 
1st, you must know the circumference of the equator.
2nd, you must know the circumference of the equator plus 2 cm above it.
It is just two circles. Figure the circles using the diameter or radius then another circle with the additional amount added to the radius or twice the amount added to the diameter. Then divide the amount by the diameter of the coin.
You should have enough information to do the problem using a calculator (it can be done with a pencil and paper).
Note: a free calculator is here:
http://www.redchillicrab.com/en/redcrab/index.html
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hope this helps
falcon
 
irene12 said:
I have an extra credit problem I can't begin to figure out. Any ideas? Thank you
Leia has enough gold coins to place them side by side and create a belt around the earth at the equator. Mike has more than enough coins to create a belt around the earth at least 2 cm above the equator. the coins are identical, with diameter 2 cm. What is the smallest number of coins by which mike 's hoard surpasses Leia's

you really don't need to know any other physical data - beyond which has been provided.

Let the radius of earth at equator = R cm

So the radius of Leia's belt = R

So the radius of Mike's belt = R+2

Circumference of Mike's belt - Circumference of Leia's belt = 2*pi*(R+2) - 2*pi*R

Now continue......
 
irene12 said:
2 cm above the equator

I'm thinking that the responses thus far differ in their interpretation of the above phrase.

Or, maybe it's just me. 8-)
 
Earth's equatorial radius: 6378.137 km
http://en.wikipedia.org/wiki/Earth_radius
Values differ per Reference.
100cm = 1 meter
1000 meters = 1km
Draw two circles (one inside the other)
The inside one is the earth
The outside is 2 cm larger
Subtract the smaller from the larger
Divide 2 cm into the difference That is the amount of coins
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The interpretation is the same
falcon
 
Thank you. I was thinking Mikael's belt was 2 cm north of the equator (above) and it was not making sense to . Irene
 
I read the problem that way too initially. It was not ideally worded
 
If you are going to continue in math, I suggest a good programmable scientific calculator with graphing capabilities.
Reason: You need to get familiar with using the calculator for more advanced math. There are several (FREE) ones on the internet with good help files or good user manuals.
Here are some free ones (downloadable). There are also several online ones. I prefer the downloadable ones.
RedCrab http://www.redchillicrab.com/en/redcrab/index.html
Precise Calculator http://preccalc.sourceforge.net/download.shtml
Graph Calc http://www.graphcalc.com/
Calculator Pro http://download.cnet.com/Calculator-Pro ... 70367.html

All have their advantages and disadvantages. Use the one you are most comfortable with.
I can get you some example programs for them if you need help using them.
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hope this helps
falcon
 
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