Question

A box with a height of 5 inches that contains 9 identical glass spheres that have a diameter of 5 inches are used to make snow globes.The spheres are tightly packed,as shown below.15 by 15 in.What is the volume of the empty space left in the box,in cubic inches?Round your answer to the nearest tenth of a cubic inch.

Answer 1

the picture in the attached figure

we know that
volume of the box=15*15*5-----> 1125 in³

the volume of one sphere=(4/3)*pi*r³
r=5/2----> 2.5 in
the volume of one sphere=(4/3)*pi*2.5³----> 65.45 in³

volume of 9 spheres=9*65.45 ----> 589.05 in³

the volume of the empty space left in the box=1125-589.05--> 535.95 in³

the answer is
536 in³