Final answer:
To find the maximum number of number cubes that can fit into each box, calculate the volume of the number cube and each box. Divide the volume of the box by the volume of the number cube to find the maximum number of cubes that can fit. For the packing plan, distribute the cubes among the box sizes based on the maximum number that can fit in each box. so she would need 0.559 of the 39-inch box.
Step-by-step explanation:
To find the maximum number of number cubes that can fit into each box, we need to calculate the volume of the number cube and the volume of each box.
The volume of a number cube is found by multiplying the length, width, and height. In this case, each side of the number cube measures 3.4 inches, so the volume is 3.4 x 3.4 x 3.4 = 39.304 cubic inches.
Now, we can calculate the maximum number of cubes that can fit into each box by dividing the volume of the box by the volume of the number cube. For the 64-inch box, the volume is 64 x 28 x 39 = 70080 cubic inches. Therefore, the maximum number of cubes that can fit into the 64-inch box is 70080 / 39.304 = 1781.
Using the same method, we find that the maximum number of cubes that can fit into the 28-inch box is 998 and the maximum number of cubes that can fit into the 39-inch box is 1395.
For the packing plan, Geraldine needs to distribute the 780 cubes among the three box sizes. She can pack 1781 cubes in the 64-inch box, so she would need 780 / 1781 = 0.438 of the 64-inch box. This means she will use 1 box of the 64-inch size.
Next, she can pack 998 cubes in the 28-inch box, so she would need 780 / 998 = 0.782 of the 28-inch box. This means she will use 1 box of the 28-inch size as well.
Finally, she can pack 1395 cubes in the 39-inch box, so she would need 780 / 1395 = 0.559 of the 39-inch box. This means she will use 1 box of the 39-inch size.