Final answer:
To estimate the number of tennis balls required to fill a classroom, you convert the room's dimensions into inches, calculate its volume, and then determine how many times the volume of a box that fits 22 balls goes into the room's volume, finally multiplying by 22 to get the estimated total number of balls.
Step-by-step explanation:
The question revolves around estimating the number of tennis balls required to fill a classroom with the given dimensions. Let's start by converting the classroom dimensions from feet to inches because the size of the box that holds 22 golf balls is in inches. There are 12 inches in a foot, so the classroom dimensions in inches are 120 inches high, 456 inches wide, and 324 inches long. Next, we calculate the volume of the classroom by multiplying these dimensions: 120 in × 456 in × 324 in which gives 17,602,560 cubic inches.
Now, we previously know that a box measuring 5 in x 13 in x 12 in can hold 22 golf balls. The volume of this box is 780 cubic inches. Assuming a tennis ball and a golf ball are approximately the same size (for estimation purposes), we can then calculate how many boxes of this size we can fit into the classroom volume by dividing the classroom volume by the box volume: 17,602,560 in³ / 780 in³.
This calculation results in approximately 22,566.36, which we round down to 22,566 since we cannot have a fraction of a box. Since each box contains 22 balls, we multiply this number by 22 to estimate the number of tennis balls needed to fill the classroom: 22,566 boxes × 22 balls/box = 496,452 balls.