Question

A box contains 9 identical glass spheres, tightly packed. The box is 12 inches by 12 inches. What is the total volume in cubic inches?

Answer 1

V(b) = 576 in³

Explanation:

9 = 3 * 3

12 = 3 * 2 *2

To have 9 spheres in a box 12 x 12 in²

We need to arrange in a grid of 3 x 3 spheres of 4" diameter, then

three rows and three columns will fit exactly i the box 12 x 12 in²

Now the height of the box need to be adequate for the diameter of the spheres ( 4 in )

Therefore the total volume of the box is:

V(b) = 12*12*4

V(b) = 576 in³