Answer:
- The number of small boxes that will fill the large box 1 = 64
- The number of small boxes that will fill the large box 2 = 56
Step-by-step explanation:
Complete Question
Items for a fundraiser are packaged in small boxes shaped like rectangular prisms that are 4.5 inches long, 4.5 inches wide, and 8 inches tall. To transport the items to an event, you want to know how many of the small boxes will fit in larger boxes. The larger boxes are available in two sizes. Large Box 1 is 24.25 inches long, 18 inches wide, and 24 inches tall. Large Box 2 is 20.5 inches long, 18.5 inches wide, and 24 inches tall. Both the small and large boxes must remain upright.
Solution
To know how many of the small boxes will fit in larger boxes, we need to obtain the volumes of the small box, large box 1 and large box 2.
Volume of a cuboid = L × W × H
For the small box,
Length = L = 4.5 inches
Width = W = 4.5 inches
Height = H = 8 inches
Volume of the small box = 4.5 × 4.5 × 8 = 162 in³
For large box 1,
Length = L = 24.25 inches
Width = W = 18 inches
Height = H = 24 inches
Volume of the large box 1 = 24.25 × 18 × 24 = 10,476 in³
For large box 2
Length = L = 20.5 inches
Width = W = 18.5 inches
Height = H = 24 inches
Volume of the large box 2 = 20.5 × 18.5 × 24 = 9,102 in³
The number of small boxes that'll fill the large box 1 = (10,476/162) = 64.667 = 64 small boxes (rounded down because the fraction cannot be forced into the large box 1.
The number of small boxes that will fill the large box 2 = (9,102/162) = 56.185 = 56 small boxes.
Hope this Helps!!!
