Number Of Tennis Balls That Can Fit In A Boeing 747

	A	C	D	E	F
1	ASSUMPTIONS:	Calculate the number of tennis balls that can fit in a Boeing 747
2	The number of seats in a Boeing 747 are 500-600.	Step 1: Calculating the total volume of Boeing 747
3	Length of the plane is ~70m.	Radius (in metre)		3
4	Assuming Beoing 747 as a cylinder, its radius is ~3m.	Length (in metre)		70
5	Radius of a tennis ball is ~3.3 cm or 0.033m.	Total Volume (πr²h) (in cubic metre)		1978.2
6	A boeing 747 has 60 rows and each row has 10 seats, 3-4-3 arrangement	% of plane that will taper in the ends		20%
7	A chair can be looked at as a combination of 2 cuboids.	Tapered area will form a cone which is one-third of cylinder		130.5612
8	Luggage area is considered empty.	Occupied space by pantry/washrooms/overhead luggage etc		40%
9	Since the balls are spherical, they lead to wastage of space between 4 balls, therefore, they are treated as cubes and not spheres	Unoccupied space (in cubic metre)		1108.58328
10		Step 2: Calculating the volume occupied by the objects inside Boeing 747
11		Dividing the plane into 3 segments	Cockpit	Seating	Luggage
12	AN OUT OF THE BOX TAKE	% of area	10%	75%	15%
13	Being spherical, tennis balls cannot fill up all of the free volume inside the plane, and only a certain percentage, say 70-75%	Volume (in cubic metre)	110.858328	831.43746	166.287492
14	Tapering of the fuselage and free volume inside empty fuel tanks can also be taken into account.	Cockpit
15		Objects inside the cockpit		Area Occupied (%)	Area Occupied (in fig.)
16		2-3 seats for the pilot		15	16.6287492
17	STRUCTURE	Instrumentation Panel		45	49.8862476
18	Total Volume of Boeing 747	Free Volume (in cubic metre)		44.3433312
19	-	Seating Area
20	Volume occupied by the objects inside the plane	Calculating the volume of one chair
21	=	Dimensions		Upper part	Lower Part
22	Volume that can be used to fit tennis balls	Length (in metre)		1	0.6
23	/	Breadth (in metre)		0.5	0.5
24	Volume of a tennis ball	Width (in metre)		0.1	0.1
25	=	Volume (in cubic metre)		0.05	0.03
26	Number of tennis balls that can fit inside a Boeing 747	Percentage increase due to legs/handle etc		20%
27		Total Volume of a single chair (in cubic metre)		0.096
28		Total volume of all chairs
29	SANITY CHECK	Number of rows	Chairs per row	Total no. of chairs	Total Volume
30	Total Volume of a Boeing 747	60	10	600	57.6
31	1978.2	Free Volume (in cubic metre)		773.83746
32	Free Volume in a Boeing 747	Luggage Area
33	984.4682832	Total Volume = Total free Volume		166.287492
34	49.77%	Step 3: Calculating total free volume in a Boeing 747
35	Number of tennis balls that can fit inside a Boeing 747	984.4682832
36	3,424,285	Step 4: Calculating the volume of a tennis ball
37	Number of tennis balls per cubic metre	Radius of a tennis ball (in metre)		0.033
38	3478	Volume of a tennis ball = (2r)^3		0.000287496
39		Step 5: Calculating the number of tennis balls that can fit inside a Boeing 747
40		Total free volume of Boeing 747 (in cubic metre)		984.4682832
41		Total volume of 1 tennis ball (in cubic metre)		0.000287496
42		Number of tennis balls that can fit inside a Boeing 747		3,424,285
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