Question

Already did work, just need to be checked.

Answer 1

Each penny is 0.75 inches in diameter and 0.061 inches thick. If the cylindrical glass jar containing the pennies has a diameter of 6 inches and a height of 11.5 inches, how many pennies can fit inside the jar?
My answer:
Cylinder: Diameter-6 in/ Height 11.5 in
V=3.14(r²)h
3.14(3²) (11.5)
3.14*9 (11.5)
Volume=324.99
Pennies: Diameter-0.75 in/ Height .061 in
V=3.14(r²)h
3.14(.375²)(0.061)
3.14*.140625 (.061)
4415625*.061
Volume=0.0269353125


324.99/0.0269353125= 12,065
pennies(approximately)
12,065 Pennies can fit in the cylinder

Answer 2

y

Answer 3

@cyter what do you mean y?

Answer 4

yes

Answer 5

again, since your value for pi is only accurate to 3 significant figures
your final answer can only be accurate to 3 sig figs
=12100 pennies (3 sig. figs.)

Answer 6

@cyter @UnkleRhaukus so it's correct then?

Answer 7

Only to three decimal places

Answer 8

yeah i think you have calculated it the right way,

[im assuming that you dont have to consider the close packing structure]

Answer 9

this is a bit more accurate

https://www.google.com/search?q=pi*(.375%C2%B2)(0.061)&oq=pi*(.375%C2%B2)(0.061)&aqs=chrome..69i57.4993j0j7&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8#es_sm=93&espv=210&q=324.99%2F(pi*(.375%5E2)(0.061))

Answer 10

Nah, just how many pennies can fit in there. @UnkleRhaukus is it okay if I give @cyter a medal since I gave you one last time?

Answer 11

sure, i dont mind

Answer 12

Thanks for helping, peoplessss!!!! I may be back on here later for more checks :)

Answer 13

Oh, I have one more question!!

Answer 14

If you were to find the empty space the pennies leave, would you just subtract the volume of the container from the pennies?

Answer 15

i think the method we've used assumed no gaps

Answer 16

yep

Answer 17

so its not very accurate , (for circles especially) .
if the gaps matter you'll have to consider the packing structure,

Answer 18

My guess is that you subtract :
324.99-0.0269353125=324.9630646875
But that doesn't make much since...
Well this is what the question states:
For the Penny Problem, how much empty space should exist inside the jar after being filled to capacity with pennies? Why doesn't this amount of space actually exist in the jar?

Answer 19

324.99-0.026935=324.963064
is the volume of the air in the jar with one penny in it

Answer 20

So just times that by how many pennies you can put in the jar as we figured out in the last problem?

Answer 21

@UnkleRhaukus ?

Answer 22

im getting confused, the true number of pennies that will fit will be less than what we calculated because the packing structure has many gaps, the volume of these gaps will be greater than the volume of a penny so the method we used will over estimate the pennies that will fit

Answer 23

Yeah... I'm way past confused... it's 2:30 am here

Answer 24

you might have to work out the most pennies that can fit in each layer
http://www2.stetson.edu/~efriedma/cirincir/
but if you haven't been studying this stuff maybe there is some other way

Answer 25

Wow, I don't think we've been studying that... I guess I'll just try and figure this out, and see what my teacher says. Thanks again!