Question

If a cylindrical can hold three balls with no room to spare, explain how to find the volume of the air that surrounds the balls in the can. Let the balls have a diameter of 6 inches.

Answer 1

can you help me @mathmale @tanya123

Answer 2

Wow I got tagged with mathmale...

Answer 3

is that bad 4 u?

Answer 4

Actually really Good, and sorry I'm not really good diameter...

Answer 5

@mathmale can you help me out please

Answer 6

Hello! Feels good to know that you want to work with me.
I'd suggest you assume that the can has almost exactly the same diameter as do the balls: 6 inches. Suppose that the can were closed at one end, and that you fill it up with three balls. If you were to put the top on, it would touch the uppermost ball, right?

Answer 7

According to this reasoning:
1) Find the volume of 3 of these balls of diameter 6 inches.
2) Find the volume of the cylindrical can.
3) Subtract your result (1) from your result (2).

Answer 8

ok

Answer 9

@Abmon98 can u help me please

Answer 10

@gswag98: ??

Can you find the volume of a ball which is 6 inches in diameter?

Answer 11

ok so #1 the volume of the balls is 36 pi which is 113.0973

Answer 12

Three of these balls lined up in a row, touching, extend 18 inches, right?

What is the volume of a cylinder of radius 3 and height 18 inches?

Answer 13

Remember: the diameter of the balls is 6 inches. The radius is less than that. What is the radius of each ball? What is the volume of each ball? (It's not 113.0973.)

Answer 14

@mathmale 162 pi the volume of the cylinder which is 508.9380099

Answer 15

Right on the volume of the cylinder, although you're going to need to round off that figure.
For the time being, find the volume of ONE of the balls. What is the ball radius?

Answer 16

one of the ball's radius is 3 and the volume is 113.0973355 for one of the ball's

Answer 17

I agree with that. What is the total volume of the three balls?

Answer 18

so do I times 3 the volume of 1 ball

Answer 19

Summary: sphere and cylinder volumes are calculated using their radii (not their diameters). So, be certain to convert "diameter" to "radius" by halving each diameter.

Answer 20

Yes, you do. 3 times approx. 113.097 is what?

Answer 21

486 pi which is 1,526.81403

Answer 22

But isn't 3 times approx. 113.097 equal to 339 something? You don't need to involve pi here, as you've found that the volume of ONE ball is 113.097 and need only multiply that by 3.

Answer 23

oh ok

Answer 24

What is the total volume of the 3 balls?

Answer 25

the total volume of the 3 balls is 339.291 right?

Answer 26

yes. write that down, please: total vol. of the 3 balls is 339.291 cubic inches.

Answer 27

ok I did that

Answer 28

Now please go back and find your figure for the volume of that 6-inch-diameter, 18-inch-long cylindrical can. The can volume is .... ?

Answer 29

so do I do the volume of cylinder formula to get the answer

Answer 30

No, because we've already gone through that. All you need to do is to review this conversation and find the volume of the cylinder from way back (in the conversation).

Answer 31

oh ok

Answer 32

The can volume is .... ?

Answer 33

the can volume is 508.9380099

Answer 34

Yes, with units of measurement "cubic inches" (mandatory).

OK. You have an empty cylindrical can of diameter 6 inches, radius 3 inches, and length/height 18 inches; its volume, empty, is about 308.938 cubic inches. Agree or disagree on that?

Answer 35

hold on I have a phone call

Answer 36

ok I think I agree on that

Answer 37

Now we put 1 ball inside the can. Will there be more or less air inside the can now?

Answer 38

less air

Answer 39

And then we put in the remaining two balls. What can you say about the volume of air still to be found inside the can?

Answer 40

is there a formula for volume of air

Answer 41

Yes and no. No specific formula! But you know the volume of the air in the can when the can has no balls in it. You also know the total volume of the three balls. So, if you put all three balls in the can, how much air is left in the can?

Answer 42

is the answer way back in the conversation

Answer 43

No. Just take the volume of the can and subtract the total volume of the 3 balls and you've got your answer. We haven't done that yet.
do it now, please.

Answer 44

gswag98 Best Response Medals 0
the can volume is 508.9380099

mathmale Medals 1
yes. write that down, please: total vol. of the 3 balls is 339.291 cubic inches.

Answer 45

@mathmale the answer would be 169.64700099

Answer 46

You are subtracting the total volume of the balls from the volume of the empty cylinder. That is appropriate. have you forgotten something?

Answer 47

ok what is it supposed to be then

Answer 48

mathmale Medals 1
Right on the volume of the cylinder, although you're going to need to round off that figure.

Answer 49

mathmale Medals 1
Yes, with units of measurement "cubic inches" (mandatory).

Answer 50

gswag98: The volume of the air in the can, surrounding the balls, is ... ??? (round off your answer to two decimal places)

Answer 51

what have I forgotten

Answer 52

You need to round off your answer and you need to include the units of measurement.
I'm not your instructor, but believe me, one of your instructors in the future is going to pick on you if you don't do both properly. Try it now.

Answer 53

Start with:

gswag98 Best Response Medals 0
@mathmale the answer would be 169.64700099

How many decimal places would you say are reasonable? Did you use pi = 3.14, 3.14159, or 22/7? Judge what degree of accuracy seems appropriate in this situation.

Answer 54

Personally I'd settle for 2 decimal places, which assumes that you and I assumed that pi equals 3.14 (with two decimal places). Round off 169.67700099 to 2 decimal places, please.

Answer 55

thank you for your patience in sticking to this problem. I know it's been a long discussion, but still a necessary one.

If you round off to two decimal places, which figure is correct? 169.67 or 169.68?

Answer 56

169.67

Answer 57

Because you have 169.677 to start with, you must round up that first 7 to an 8 because of the second 7.

169.68.

169.68 what? what are the appropriate units of measurement?

Answer 58

169.68 cubic inches

Answer 59

Beautiful. Please, review this conversation and refresh your memory on how we arrived at 169.68 cubic inches. We covered quite a few concepts here.

Answer 60

sorry the conversation has been so long, but I really do not see any important way in which you would have learned as much with less discussion.

Answer 61

Where do we stand now? Are you OK with this solution? Have any questions or comments?

Answer 62

Nice working with you. I'm leaving this conversation now, since I believe we're finished and you are "just looking around," according to OpenStudy. Best wishes to you.

Answer 63

no I'm on this conversation

Answer 64

I'd much rather take your word for that than OpenStudy's word!

Answer 65

Any comments or questions before we end this conversation?

Answer 66

no

Answer 67

Hope to work with y ou again, gswag98. Good luck!

Answer 68

THANK YOU @mathmale soooo much

Answer 69

My pleasure! Bye, gswag88. Hang in there.
Over and out.