Final answer:
By dividing the box dimensions by the tennis ball diameter and only considering whole balls that can fit, we can determine that 12 tennis balls will fit in the box with dimensions 12" x 5" x 10", when the tennis ball diameter is 2.63 inches.
Step-by-step explanation:
To determine how many tennis balls will fit in a box with dimensions 12" x 5" x 10", we first have to understand the packing dynamics of spheres within a rectangular prism. Each tennis ball has a diameter of 2.63 inches, so the radius is 1.315 inches.
We begin by calculating how many balls can be placed along each dimension:
- The box is 12 inches long. Dividing this by the diameter of a tennis ball gives us approximately 4.56, which means we can fit 4 balls along the length comfortably without compression.
- The box is 5 inches wide. Dividing this by the diameter of the tennis ball gives approximately 1.90, which allows us to fit 1 ball along the width.
- The box is 10 inches high. Dividing this by the diameter of the ball gives us approximately 3.80, which means we can fit 3 balls along the height.
Now, we calculate the total number of balls by multiplying the number of balls that can be fitted along each dimension:
4 (length) x 1 (width) x 3 (height) = 12 tennis balls
Note that any fractional part of a ball cannot count as a full ball, hence why we only counted whole numbers for each dimension. This calculation assumes a simple cubic packing which generally is not the most efficient packing for spheres, but without additional packing details, it is the most straight-forward approximation.