Question

To start off the challenge, the radio station has placed pennies in a cylindrical glass jar. 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? You must show all work to receive credit.

Answer 1

theres a few ways we can do this, the simplest way is to determine the volume of each penny and divide the volume of the jar by the volume of the penny to = how many pennies can fit.

Answer 2

of course pennies are not liquid

Answer 3

so it wouldnt be exactly accurate to say that.

Answer 4

okay so what should I do

Answer 5

first calculate the volume of a penny so a penny is a cylinder shape.

Answer 6

V=pi(radius)^2(height)

Answer 7

I got 325.15 and 269.49 are those right?

Answer 8

well the diameter of a penny is 0.75 inches, so the radius would be half that, so 0.375 inches

Answer 9

the height or (thickness) is 0.061 inches

Answer 10

were those volume right?? haha

Answer 11

\[Volume=\pi(0.375)^2(0.061)\]

Answer 12

so no, the volume of a penny is approximately 0.027 inches cubed

Answer 13

got 26.93.....

Answer 14

\[\pi \times 0.140625 \times 0.061\]

Answer 15

the 0.140625 = 0.375^2

Answer 16

oh okay

Answer 17

what about the next volume I have to find what do I plug in for that

Answer 18

so the jar is also a cylinder.

with diameter 6 and radius is half the diameter so the radius is 3.

height is 11.5 inches

Answer 19

so how would I plug that in the formula

Answer 20

volume = pi times height times radius squared

\[\pi \times 11.5 \times 3^2\]

Answer 21

so 324.99?

Answer 22

i get 325.15

Answer 23

how? I did 3.14x11.5x3x3

Answer 24

pi is a bit longer then 3.14, i used the alot more decimal places
3.1415926535897932384626433832795

Answer 25

infact its infinitely longer

Answer 26

oh okay

Answer 27

so then what are the two volumes again? because I know u divide the bigger by the smaller one

Answer 28

yes

Answer 29

so what were the two volumes??

Answer 30

0.027 inches cubed and 325.15 inches cubed

Answer 31

but dont pay attention to the cubed part just divide 325.15/0.027

Answer 32

okay thank you so much!!! and I have another question that gos with this

Answer 33

the thing is, you should say this is the answer if we dont factor in the spacing between pennies. that would be alot more work, and your teacher probably isnt expecting you to do all that anyway.

Answer 34

1.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 35

well what we basically said when we did the volumes and divided them is.

is you take 12042.59 pennies, and melt them down into a liquid, pour the liquid into the jar and the jar would be full.
so in this case, there is no air in the jar, its perfectly filled up.

Answer 36

okay and one more question

Answer 37

i think ill leave the rest for you to do, cant just give out all the answers