6.) Find the order of magnitude of the number of table tennis balls that would f
ID: 2044799 • Letter: 6
Question
6.) Find the order of magnitude of the number of table tennis balls that would fit into a typical size room(without being crushed). In your solution, state the quantities you measure or estimate the values you took for them.
7.) Compute the order of magnitude of the mass of a bathtub half full of water. Compute the order of magnitude of the mass of a bathtub half full of pennies. In your solution, state the quantities you measure or estimate the values you took for them.
10.) A child is surprised that she must pay $1.36 for a toy marked $1.25 because of sales tax. What is the effective tax rate on this purchase, expressed as a percentage?
Explanation / Answer
6. volume of pingpong ball = 4/3 p 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( p 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. 7. Well... I'd ESTIMATE that a bathtub holds 40 gallons of water. So a tub half full would be 20 gallons. I happen to know that a gallon of water weighs around 8 pounds (you could look up an exact conversion) so my order of magnitude estimate would be 20 * 8 = 160 pounds. I'll assume pennies are solid copper (they're not). I looked up copper and found it has a density of 8.92 gm/cm^3 which converts to 74.4 pounds per gallon. But the pennies wouldn't totally fill the space in the tub - there would be some "voids" between them. I might ESTIMATE that there's an 80% fill so I'd calculate the order of magnitude estimate of the mass as 20 gallons * 74.4 pounds/gallon * 0.8 fill = 1190 pounds. 10. Try thinking about how tax is computed. r = 0.11/1.25 = 8.8%
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