Your teacher made the comment that more than 100, 00 ping pong balls would fit in the school gym. develop a calculation method to see if she is right. after taking some measurements, propose the amount the gym would hold. i din't really understand how to solve the scenario above.
Divide the volume of the gym by the volume of a ping pong ball.
so if the volume of the gym is 63480 and the volume of the ping pong ball was 2. 045 would the amount of ping pong balls be 31041 ping pongs
Yes, if you're using the same units.
However, the school gym has a volume of at least 100,000 cubic feet. That's 172,800,000 cubic inches. The volume of a ping pong ball is about 2.045 cubic inches.
172,800,000 / 2.045 = ?
84498777.51
which is 7041564.7925 ft
ft?
You need to find how many ping pong balls fit in the gym.
84,498,777 ping pall balls will fit in this gym.
the official radius of a ping pong ball is 20 mm or 2 cm
so the volume of a ball is (4/3)π(2^3) = appr 33.5 cm^3. which Ms Sue has correctly as 2.045 inches^3
but the balls will not "stack" nicely.
Did you ever look at a stack of cannonballs at some fort?
If we pile them nicely on top of each others to form nice simple columns, each ball would occupy appr 3.9 inches^3 , (.7874)^3)
and using Ms Sue's guess of 100,000 cubic ft or
100,000(12^3) cubic inches we could get
172,800,000/2.045= 84,500,000 balls to the nearest 100,000
If we allow then to stack the way cannonballs would stack, the space between them would be less and we would get more into the same space.
However, that would be a very messy kind of a problem
Adjust your calculation once you know the dimensions of the gym.