A baseball has a diameter of 6.2cm. They are packed in a cardboard box that is just large enough to hold 12 baseballs. What are the possible dimensions?

Question

What shape is the box?

what is the volume of the 12 baseballs?

how much airspace is there inside the box?

Answer 1

The total volume of the baseballs (radius 3.1 cm) can be found by multiplying the volume of one baseball (4/3)*pi*r^3 by 12:

(4/3) * pi * r^3 = (4/3)*3.14159* (3.1)^3 = (4/3)*3.14159*29.791 = 124.788 cu cm for one ball

The volume of 12 of these would be 124.788*12 = 1497.46 cu cm

possible dimensions:

1 row of 12 balls:  74.4 cm (6.2*12) by 6.2 cm by 6.2 cm=2859.936 cu cm ;  airspace in box = total box volume-total baseball volume=2859.936 cu cm -1497.46 cu cm= 1362.476 cu cm

 

2 rows of 6 balls: 12.4 cm (6.2*6) by 37.2 cm (6.2*6) by 6.2 cm=2859.936 cu cm ; airspace in box = total box volume-total baseball volume=2859.936 cu cm -1497.46 cu cm= 1362.476 cu cm

 

3 rows of 4 balls: 24.8 cm (6.2*4) by 18.6 cm (6.2*3) by 6.2 cm=2859.936 cu cm; airspace in box = total box volume-total baseball volume=2859.936 cu cm -1497.46 cu cm= 1362.476 cu cm

 

2 levels of 2 rows of 3 balls:  12.4 cm (6.2*2) by 18.6 cm (6.2*3) by 12.4 cm (6.2*2) = 2859.936 cu cm; airspace in box = total box volume-total baseball volume=2859.936 cu cm -1497.46 cu cm= 1362.476 cu cm

 

I hope this helps....