Question

Fan&Medal

Answer 1

http://prntscr.com/4i5ao2

Answer 2

@ganeshie8 @kropot72 @Hero

Answer 3

@myininaya @Preetha @nincompoop

Answer 4

@tkhunny

Answer 5

Is there a question? Show your work.

Answer 6

http://prntscr.com/4i5agh http://prntscr.com/4i5akp http://prntscr.com/4i5ao2

i already did the challenges all i need is the 1-5 questions
@tkhunny

Answer 7

Great. Let's see your work!

Answer 8

1. First to find the volume of a penny you us the formula “3.14*r2*h” and plug .75 and .61 in it and get 3.14*.75/2)^2*.61 and get 0.0269.

First we use the formula 3.14XR^2XH. So b/c the diameter is 6 you divide and get 3 and put in formula 3.14*3^2*11.5. I got 324.99 and I round and got 325. Then you divide 325 and 0.0269 and I got 12081.

2. First you put in three different formula
Cone: 1/3 bh so 1/3 X 3.14 X13/2^2X 44-36
1/3X 3.14 X 6.5^2 X 8= 353.77
Cylinder: diameter 13 height 36 so 3.14 13/2^2 36 =4776
Ball: 4/3 3.14 r3 so 4/3 X 3.14 (2.63/2)^3
4/3 X 3.14(1.315)^3=1.66
3. Sphere = (4/3)Pi r^3 V = (4/3)Pi * 17.25 V = 21500.9 inches cubed
Pyramid = (1/3)w^2*h V = (1/3) * 1*1 * 0.75 V = 0.25 inches cubed
21500.9/0.25 = 86003.6
Therefore it will fit approximately 86003 pieces of gum

Answer 9

@tkhunny

Answer 10

@e.mccormick

Answer 11

@charlotte123 @iPwnBunnies @triciaal @jdoe0001

Answer 12

Well, like we talked about, by basic math there is no empty space. However, in real life there would be gaps around the pennies. With just geometry, you can't easily estimate these gaps so it does not show up in the answer.

Answer 13

For the second one, think about the volume of a box. Also, remember when we talked about how a cone has b for base as part of the volume? What was that base? It had another formula.

Answer 14

now i mean the questions 1-5 @e.mccormick

Answer 15

Yes. #1 talks about the coin jar again. #2 asks about where the volume of a cylinder came from.

Answer 16

isnt #1 same answer as challenge one

Answer 17

@e.mccormick

Answer 18

Not really. It is asking about the empty space, which is the flaw in doing this with just geometry. It is really hard to find an emty space with thousands of items involeved with geometry.

Answer 19

@jagr2713 how many pennies did you put in the jar?

Answer 20

heres what i did for the challenges

Answer 21

First to find the volume of a penny you us the formula “3.14*r2*h” and plug .75 and .61 in it and get 3.14*.75/2)^2*.61 and get 0.0269. First we use the formula 3.14XR^2XH. So b/c the diameter is 6 you divide and get 3 and put in formula 3.14*3^2*11.5. I got 324.99 and I round and got 325. Then you divide 325 and 0.0269 and I got 12081. 2. First you put in three different formula Cone: 1/3 bh so 1/3 X 3.14 X13/2^2X 44-36 1/3X 3.14 X 6.5^2 X 8= 353.77 Cylinder: diameter 13 height 36 so 3.14 13/2^2 36 =4776 Ball: 4/3 3.14 r3 so 4/3 X 3.14 (2.63/2)^3 4/3 X 3.14(1.315)^3=1.66 3. Sphere = (4/3)Pi r^3 V = (4/3)Pi * 17.25 V = 21500.9 inches cubed Pyramid = (1/3)w^2*h V = (1/3) * 1*1 * 0.75 V = 0.25 inches cubed 21500.9/0.25 = 86003.6 Therefore it will fit approximately 86003 pieces of gum

Answer 22

@jagr2713 what does pieces of gum have to do with how many pennies you can fit in the jar? as before how many pennies are in the jar? For question #1 how do you explain the amount of empty space that should exist but is not really there?

Answer 23

i got 0.0269

Answer 24

Well, if you pathologically use 3.14 for \(\pi\), you will be underestimating your penny volume. 1 penny? So what? I jar full of a few 1000? That's a problem.

\(\pi r^{2}h\) with r = 0.75/2 and h = 0.61

If we are sticking with 2 significant digits, t = 0.38

3.145*.385^2*.615 = 0.287
3.135*.375^2*.605 = 0.268

That's quite a difference. 0.019/penny * 2000 pennies = 38 You've an awful lot of slack in this system.

Anyway, you can't find the projected extra volume because pennies don't fit perfectly. You'll waste more than projected.

Answer 25

ok so can you help with numbers 345 i did 1&2

Answer 26

@tkhunny

Answer 27

I'm actually afraid of #3. It is quite ambiguous. There are relatively simple Calculus answers, but these volumes were known long before the Calculus was invented. So, "Where these derive from?" I do not think the question has a unique answer.

Answer 28

Yah, this is a geometry problem that is asking for calculus answers. LOL. But, for #3 if you think about the relationship between a triangle and a square, you can see that there is some sort of relationship between say a cone (rotated triangle) and a line (base of a square or triangle).