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How many balls does it take to fill a 16x16 ft room?

asked in Estimation by (40 points)
edited by | 439 views
+1

Equation:

No of basketballs that can be accommodated in a 16X16 room is = ( Available Volume of the room / Volume of each basketball )

Assumptions and Facts:

  1. We are assuming that, its the basketball we are talking about in this case study. Size of the ball is assumed to be of radius 15 cms.
  2. The room is assumed to be of a cube size. So height, width and length all are assumed to be 16 ft.
  3. The best possible fit ratio is assumed to be 75%. So only 75% of the room is available for fitting basketballs in it.
  4. 1 ft = 30 cms (fact)

Process:

Volume of a Room can be calculated by formula = Length * Breadth * Height

Total space in room in cms cube (A) = 16 * 16 * 16 * 30 * 30 * 30

Calculation of available space in room (B) = 0.75 * A

Volume of each ball = Volume of each sphere = (4/3) * (22/7) * cube of radius

Volume of each ball (C) = (4/3) * (22/7) * 15 * 15 * 15

Dividing B by C, you should get around 6300, which means we can fit in approximately 6300 basketballs in a room of dimensions 16 ft X 16 ft X 16 ft

+1
As there's always a space between the balls, I think it would be much easier to treat the balls as cubes in the first place, thus not calculate sphere volumes.

1 Answer

0 votes
Clarify the question:

Is the room empty or it has furniture.

Are the balls arranged properly or just thrown in randomly

What kind of ball it is - golf, tennis, basketball?

Assumptions and Facts:

Room is empty

Ball - Tennis ball

Balls will be stacked perfectly

Equation:

No. of balls = Volume of room/ Volume of ball

Computation:

Volume of room = 16*16*12 = 3072 cubic feet (assuming empty) = 3072*1728 = 5300000 cubic inch

Volume of ball - assuming square volume of side 2.5 inch - 15.62 cubic inch

Edge cases:

Windows

Furniture

Other equipment

Ceiling top layer

Final computation:

5300000/15.62  = 3,39000 approx (Tennis balls with empty room stacked properly)

if furniture = 307000 approx
answered by (13 points)

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