Maximizing Space: Estimating the Number of Ping-Pong Balls in a Room

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Another possibility is that you're using the wrong units. Your answer needs to be in the same units as the question (cm^3).It sounds like you are doing the math correctly, but the program is not recognizing your answer as being within the correct range. I suggest double checking your calculations and units, and perhaps rounding your answer to the nearest order of magnitude.
  • #1
albinoboy
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Homework Statement


Estimate the number of Ping - Pong balls that would fit into a typical-size room (without being crushed). In your solution state the quantities you measure or estimate and the values you take for them. (Assume 25% of the space cannot be filled due to spherical packing.)

(a) Find the volume of the room (in m^3)

(b) Find the volume of a ball (in cm^3)

(c) Find the number of balls (order of magnitude only) (balls)


Homework Equations


75% of 1000m^3 = 750m^3
750m^3(1 000 000 cm^3/1m^3)


The Attempt at a Solution


(a)I said that an average room had 1000m^3
It said "Your response differs from the correct answer by orders of magnitude."

(b) I said the volume of a ball had 100cm^3
It said "Your response differs from the correct answer by more than 100%."

(c) I said the number of balls equaled 7.5e6
It said "Your response differs from the correct answer by more than 100%."

Any help would be greatly appreciated!
 
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  • #2
Anyone?
 
  • #3
a) Do you really think a typical room is 1000m^3? that would be 20 x 20 x 2.5 m^3
b) google for "size of pingpong ball". Use formula for volume of sphere.
 
  • #4
volume of pingpong ball = 4/3[tex]\pi[/tex]r3

Volume of room = Length*Width*Height

let's say that a standard room has a length of 7m width of 4m and a height of 2.5m. and the diameter of a pingpong ball is 4cm or 0.04m.

Volume of room = 7*4*2.5 = 70m^2
Volume of room @ 75% = 70*0.75 = 52.5m^3

volume of a pingpong ball = 4/3([tex]\pi[/tex]0.02^3)
= 0.0000335m^3

Fitting pingpong balls into room = volume of room / volume of pingpong ball.
= 52.5/0.0000335
= 1,567,164 ping pong balls.
 
  • #5
Sirsh said:
volume of pingpong ball = 4/3[tex]\pi[/tex]r3

Volume of room = Length*Width*Height

let's say that a standard room has a length of 7m width of 4m and a height of 2.5m. and the diameter of a pingpong ball is 4cm or 0.04m.

Volume of room = 7*4*2.5 = 70m^2
Volume of room @ 75% = 70*0.75 = 52.5m^3

volume of a pingpong ball = 4/3([tex]\pi[/tex]0.02^3)
= 0.0000335m^3

Fitting pingpong balls into room = volume of room / volume of pingpong ball.
= 52.5/0.0000335
= 1,567,164 ping pong balls.


All of this was very helpful. I did the math on my own and my answer matched yours. I went to enter it in and this is what I got.

Attempt 1:
(c) Find the number of balls (order of magnitude only)
1.56e6 Balls
Your response differs from the correct answer by 10% to 100%.

Attempt 2: (I tried rounding)
(c) Find the number of balls (order of magnitude only)
1.57e6 Balls
Your response differs from the correct answer by 10% to 100%.

I only have one more shot at the answer and I know I am correct with the math. What am I doing wrong?
 
  • #6
Do they not state the size of the room? and specific size of the ball? that's probably why the answers are wrong, because the values we're using are just random.
 
  • #7
Sirsh said:
volume of pingpong ball = 4/3[tex]\pi[/tex]r3

Volume of room = Length*Width*Height

let's say that a standard room has a length of 7m width of 4m and a height of 2.5m. and the diameter of a pingpong ball is 4cm or 0.04m.

Volume of room = 7*4*2.5 = 70m^2
Volume of room @ 75% = 70*0.75 = 52.5m^3

volume of a pingpong ball = 4/3([tex]\pi[/tex]0.02^3)
= 0.0000335m^3

Fitting pingpong balls into room = volume of room / volume of pingpong ball.
= 52.5/0.0000335
= 1,567,164 ping pong balls.

Sirsh, this is in violation of https://www.physicsforums.com/showthread.php?t=5374".
On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.
Please avoid this in the future.
 
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  • #8
DaveC426913 said:
Sirsh, this is in violation of PF rules

I'll be sure to not let it happen again.
 
  • #9
albinoboy said:
Attempt 1:
(c) Find the number of balls (order of magnitude only)
1.56e6 Balls
Your response differs from the correct answer by 10% to 100%.

Attempt 2: (I tried rounding)
(c) Find the number of balls (order of magnitude only)
1.57e6 Balls
Your response differs from the correct answer by 10% to 100%.

I only have one more shot at the answer and I know I am correct with the math. What am I doing wrong?

I haven't gone through the math myself. But one thing I've noticed that might help is that the program stipulated in the question (c) "order of magnitude only". However you have mentioned that you were entering things like "1.57e6". That's far more precise than just the order of magnitude.
 
  • #10
albinoboy said:
Attempt 1:
(c) Find the number of balls (order of magnitude only)
1.56e6 Balls
Your response differs from the correct answer by 10% to 100%.

That's an epic programming fail. The question asks for an order of magnitude. 10-100% is clearly within an order of magnitude.
 
  • #11
I think the issue here is answer format. A correct answer would be written as " ~ 10x #/balls in a room of x*y*z size ", where x clearly denotes the order of magnitude on base-10. Still seems like a sensitive answer to write in online submission though. Note that x #/ping pong balls is clearly separate from volume.
 

1. What is the purpose of having ping-pong balls in a room?

The purpose of having ping-pong balls in a room is usually for recreational purposes, specifically for playing the game of ping-pong.

2. How many ping-pong balls can fit in a room?

The number of ping-pong balls that can fit in a room depends on the size of the room and the size of the ping-pong balls. A standard-sized ping-pong ball has a diameter of 40 mm, so to calculate the volume of the room in cubic millimeters and divide it by the volume of a ping-pong ball. This will give you an estimate of the maximum number of ping-pong balls that can fit in the room.

3. Can ping-pong balls affect the air quality in a room?

Yes, ping-pong balls can affect the air quality in a room if there are a large number of them. Since ping-pong balls are made of plastic, they can release small amounts of volatile organic compounds (VOCs) into the air, which can affect the air quality if inhaled in large quantities.

4. Why do ping-pong balls bounce so well on hard surfaces?

Ping-pong balls are made of a lightweight and highly elastic material called celluloid. This material allows the ball to compress and deform when it hits a hard surface, storing energy in the process. When the ball bounces back, this stored energy is released, resulting in a high bounce.

5. Can ping-pong balls be used for any other purposes besides playing ping-pong?

Yes, ping-pong balls have various other uses besides playing ping-pong. They can be used for science experiments, arts and crafts, and even as a tool for massaging sore muscles. Some people also use them as decorations or for sensory play activities for children.

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