Final answer:
Approximately 22,112 ping pong balls can fit into a 1 cubic meter box when considering the packing density, hence the answer is D) More than 100.
Step-by-step explanation:
To determine how many ping pong balls can fit in a 1 unit x 1 unit x 1 unit cube, we must consider the volume of each ping pong ball and the total volume available in the cube. Given that a standard ping pong ball has a diameter of 40 millimeters, or 4 centimeters, its radius is 2 centimeters. Using the formula for the volume of a sphere, V = 4/3 πr3, we find that a single ping pong ball occupies approximately 33.51 cubic centimeters. Since there are 1 million cubic centimeters in a 1 cubic meter box (1 unit x 1 unit x 1 unit), we need more than 100 words to explain the next steps.
Without considering the packing efficiency, we can simply divide the cubic box's volume by the volume of one ping pong ball. Doing this, we find that around 29,881 (1,000,000 / 33.51) balls would fit into the box. However, because spheres do not fit perfectly together and there are spaces between them when packed, we must account for this. Assuming the most efficient packing density for spheres, which is about 74%, we would multiply the number of balls by this percentage. This results in approximately 22,112 ping pong balls fitting into a 1 cubic meter box. Hence, the correct answer to the question is D) More than 100.