Jim and Rose love to play dominoes together. They have a total of 91 dominoes. Jim is going to make a custom storage box for them. Each domino is sized: 2 in x 1 in x 3/8 in. He will make the box in the shape of a cuboid with a base rectangle of dimensions 4.2 in x 6.2 in. What should be the box's minimum depth to hold all 91 dominoes?

a) 2.5 inches
b) 3 inches
c) 3.5 inches
d) 4 inches

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.