Question

Can you show me how to solve? Don't answer. Just show me the steps.

Answer 1

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?

Answer 2

Do I solve for the cylinder and the pennies than subtract? I'm not sure, I just want to make sure I am doing it right. I don't understand geometry all that well but im trying

Answer 3

This is as far as I got:
V of sphere = 4/3 (3.14)r^3
4/3 (3.14)(.375)^3
1.3(3.14)(.375)^3
1.53075^3
3.586846606296875
Someone please help me.

Answer 4

the jar is a cylinder, not a sphere

Answer 5

if you stack the pennies perfectly, they form a cylinder

Answer 6

so do I use v= (3.14)r^2(h) instead?

Answer 7

correct

Answer 8

This is very difficult to do correctly, Stacking pennies will give you cylinders, and you can play with the footprint of the pennies on the floor of the jar, but you can see that there is a lot of air space that will remain. I do not know the answer. Alternatively, you can shake them up and hope to fill space better than with the cylinders.

Answer 9

like this ?
V of cylinder = (3.14)r^2(h)
(3.14)(3)^2(11.5)
3.14(6)(11.5)
216.66

Answer 10

3^2 is not 6

Answer 11

3^2 means "3 squared" and NOT "3 times 2"

Answer 12

oh thank you, then the final answer woul be 324.99 right?

Answer 13

that's the volume of the entire jar

Answer 14

what's the volume of a single penny?

Answer 15

each penny is a cylinder on its own

Answer 16

that's what I thought this was?
V of sphere = 4/3 (3.14)r^3
4/3 (3.14)(.375)^3
1.3(3.14)(.375)^3
1.53075^3
3.586846606296875

Answer 17

the pennies aren't spheres

Answer 18

the jar isn't a sphere either

Answer 19

Then what would the formula be fore the pennies???

Answer 20

same cylinder formula (just different radius and height)

Answer 21

both are cylinders

Answer 22

oh ok
like this
V of pennies = (3.14)r^2(h)
(3.14)(0.375)^2(0.061)
(3.14)(0.140625)(0.061)
0.0269353125

Answer 23

I can't draw, but imagine looking straight down (from a birds eye view) into the jar

this is what you'd see

Answer 24

Notice the empty spaces, I'll come back to this in a sec

Answer 25

So the volume of the jar is roughly 324.99

the volume of a single penny is 0.0269353125

Answer 26

Divide the two:

324.99/0.0269353125 = 12,065.5737704918


then round down to the nearest whole number to get 12,065

Answer 27

Years ago I did some serious study of the math associated with packing of objects into confined volumes. This question is nol suitable for the students, I suspect. The closest packing of the circles on the bottom of the jar is a good approach but not demonstrably the closest packing obtainable.

Answer 28

so if you were to melt down each penny into a liquid, then pour all of that liquid into the jar, you could fit in about 12,065 pennies

Answer 29

however, in my drawing we have solid circles that touch each other and form empty space

so you'll have room for less than 12,065 pennies (not sure how much more less)

Answer 30

oh wow. Thank you so much. I think I understand a bit better. :)

Answer 31

but 12,065 is definitely the highest you can go

Answer 32

you're welcome, I'm glad it's clicking now

Answer 33

Thank you. :)