To determine how many bowling balls the tray can hold, we first need to know the diameter of a standard bowling ball. The circumference of a bowling ball is given as 27 inches.
We can calculate the diameter (d) using the formula for the circumference (C): \[ C = \pi d \] Solving for d, we get: \[ d = \frac{C}{\pi} = \frac{27}{\pi} \approx \frac{27}{3.14} \approx 8.6 \text{ inches} \]
Next, given the tray's dimensions of 19 inches in width and 61 inches in length, we can determine how many bowling balls fit in the width and length of the tray. Since the balls are arranged in rows, we will consider how many can fit in both dimensions:
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Fit along the width: The number of balls that can fit along the width is calculated by dividing the width of the tray by the diameter of the ball: \[ \text{Number of balls along width} = \frac{19}{8.6} \approx 2.2 \] Since we can't have a partial ball, this means 2 balls fit along the width.
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Fit along the length: The number of balls that can fit along the length is: \[ \text{Number of balls along length} = \frac{61}{8.6} \approx 7.1 \] Again, rounding down, this means 7 balls fit along the length.
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Total capacity: Since the return machine can hold 2 rows of balls, we multiply the number of balls that can fit in one row by 2: \[ \text{Total balls} = 2 \text{ (width)} \times 7 \text{ (length)} \times 2 \text{ (rows)} = 28 \]
However, if we only need the total number of balls held in a single tray without distinguishing the rows, we simply calculate: \[ \text{Total balls in one row} = 2 \times 7 = 14 \]
Thus, the tray can hold a total of 14 bowling balls.
The answer to the question is 14.