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?



A)156

B)312

C) 624

D) 2496

I thought you said these problems were all different. They look exactly the same to me.

Figure the volume of one of the small blocks, and use that to divide into the whole volume.

3 1/4 = 13/4 so the box has a volume of 13/4 * 3 * 1 = 39/4 ft^3

each small block has a volume of (1/4)^3 = 1/64 ft^3

(39/4) / (1/64) = 624

Thank you for explaining.

First, find the volume of the box by multiplying its length, width, and height.

Volume = Length × Width × Height
Volume = 3 1/4 ft × 3 ft × 1 ft

To multiply mixed numbers, convert them to improper fractions.
3 1/4 ft = (4 × 3 + 1) / 4 = 13/4 ft

Volume = 13/4 ft × 3 ft × 1 ft
Volume = (13 × 3 × 1) / (4 × 1) = 39/4 ft^3

Since each foam block is a cube with 1/4 ft edge length, we can calculate the volume of one foam block.

Volume of one foam block = Edge Length × Edge Length × Edge Length
Volume of one foam block = 1/4 ft × 1/4 ft × 1/4 ft
Volume of one foam block = 1/64 ft^3

Now, divide the volume of the box by the volume of one foam block to find the number of blocks that can fit.

Number of blocks = Volume of the box / Volume of one foam block
Number of blocks = (39/4 ft^3) / (1/64 ft^3)

To divide by a fraction, multiply by its reciprocal.

Number of blocks = (39/4 ft^3) × (64 ft^3/1)
Number of blocks = (39 × 64) / (4 × 1)
Number of blocks = 2496 / 4
Number of blocks = 624

Therefore, the answer is C) 624.

To find out how many foam blocks can fit into the box, we need to calculate the volume of the box and the volume of each foam block.

The volume of the box can be calculated by multiplying its length, width, and height together:
Volume of box = Length * Width * Height

The length of the box is given as 3 1/4 ft, which can be expressed as 13/4 ft. The width is given as 3 ft, and the height is given as 1 ft.

Volume of box = (13/4) ft * 3 ft * 1 ft
Volume of box = 39/4 ft^3

The volume of each foam block is given as a cube with 1/4 ft edge length. To calculate the volume of a cube, we multiply the edge length by itself three times:
Volume of foam block = Edge length * Edge length * Edge length

Volume of foam block = (1/4) ft * (1/4) ft * (1/4) ft
Volume of foam block = 1/64 ft^3

Now, to find the number of blocks that can fit into the box, we divide the volume of the box by the volume of each foam block:
Number of blocks = Volume of box / Volume of foam block

Number of blocks = (39/4 ft^3) / (1/64 ft^3)
Number of blocks = (39/4) / (1/64)
Number of blocks = (39/4) * (64/1)
Number of blocks = 624

Therefore, the answer is C) 624.