Tasha has foam blocks stored in a box that measures 3 1/4 ft long by 3 ft wide by 1 ft tall. Each foam block is a cube with 1/4 -ft edge length. How many blocks can fit into the box?
156
312
624
2496
since the small blocks fit evenly into the large block, the large block, in small block units, is 13x12x4 units.
Or, get the number of small units by dividing volumes:
(3 1/4)(3)(1) / (1/4)
Vb = L*W*h = 13/4*3*1 = 39/4 = 9 3/4 Ft^3.
Vc = L*W*h = 1/4*1/4*1/4 = 1/64 Ft^3.
Vb/Vc = (39/4)/(1/64) = 39/4 * 64/1 = 624 blocks.
To find out how many blocks can fit into the box, we need to calculate the volume of the box and then divide it by the volume of each foam block.
The box measures 3 1/4 ft long, 3 ft wide, and 1 ft tall. To calculate the volume of the box, we multiply these dimensions together:
Volume of the box = (3 1/4 ft) × (3 ft) × (1 ft)
To simplify, we convert the mixed number 3 1/4 into an improper fraction:
3 1/4 = 13/4
Now we can calculate the volume:
Volume = (13/4 ft) × (3 ft) × (1 ft)
Volume = (39/4 ft²) × (1 ft)
Volume = 39/4 ft³
Now we need to calculate the volume of each foam block. Each block is a cube with an edge length of 1/4 ft. To calculate the volume, we cube the edge length:
Volume of each foam block = (1/4 ft) × (1/4 ft) × (1/4 ft)
Volume of each foam block = 1/64 ft³
Finally, to find out how many blocks can fit into the box, we divide the volume of the box by the volume of each foam block:
Number of blocks = (39/4 ft³) ÷ (1/64 ft³)
Number of blocks = (39/4) × (64/1)
Number of blocks = (39 × 64) ÷ 4
Number of blocks = 2496
Therefore, the answer is 2496.