Final answer:
To determine how many foam blocks can fit into the box, we calculate the box's volume and the block's volume. We find that each foam block is too large to fit inside the box, as the block's volume exceeds the box's volume, so no full blocks can fit.
Step-by-step explanation:
The question involves finding out how many foam blocks can fit inside a box based on their dimensions. To answer this, we need to calculate the volume of both the box and the individual foam block and then determine how many times the block's volume can fit into the box's volume.
First, let's calculate the box's volume. The dimensions given are 214 ft long, 2 ft wide, and 2 ft tall. The volume of the box (Vbox) is
Vbox = length × width × height = 214 ft × 2 ft × 2 ft = 856 cubic feet.
Next, we calculate the volume of a single foam block. Since each foam block is a cube with an edge length of 12 ft, its volume (Vblock) will be
Vblock = edge length3 = 12 ft × 12 ft × 12 ft = 1728 cubic feet.
Now, to find out how many blocks can fit into the box, we divide the box's volume by the block's volume:
Number of blocks = Vbox / Vblock = 856 cubic feet / 1728 cubic feet = 0.495 blocks.
Since we can't have a fraction of a block, we must round down to the nearest whole number, which means no full foam blocks can fit into the box given their sizes. This might seem counterintuitive, but it's because the dimensions of the foam block are larger than the dimensions of the box, preventing even a single block from fitting inside it.