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Answer :
Final answer:
To find the minimum depth of the box to hold all 91 dominoes, calculate the total dominoes' volume and the box's available space. The minimum depth needed is around 2.5 inches. The correct option is (a).
Explanation:
To determine the minimum depth of the box for it to hold all 91 dominoes, we need to calculate the total volume of the dominoes and the available space in the box.
First, calculate the volume of the dominoes: Volume of one domino = 2 in x 1 in x 3/8 in
- Volume of one domino = 2 x 1 x 3/8 = 3/4 in³
Now, calculate the total volume of 91 dominoes:
- Total volume of 91 dominoes = 91 x (3/4) in³ = 273/4 in³ = 68.25 in³
Lastly, calculate the minimum depth needed for the box:
- Volume of the box = 4.2 in x 6.2 in x Depth
- Given: Volume of the box = 26.04 in³, Total volume needed = 68.25 in³
- Depth = 68.25 in³ / (4.2 in x 6.2 in) ≈ 2.5 inches
Therefore, the minimum depth for the box to hold all 91 dominoes is approximately 2.5 inches.
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