Small cubes with edge lengths of 1/2 will be packed into a rectangular prism. The lenght is 4 1/2 in. With:5 in..Height:3 3/4 in...
HOW MANY SMALL CUBES ARE NEEDED TO FILL COMPLETLY THE PRISM
4 1/2 = 9 * 1/2
5 = 10 * 1/2
3 3/4 = 7 1/2 * 1/2
That means that there is some leftover space at the top. The space used is thus
9x10x7 cubes = 630 cubes
The prism cannot be completely filled unless either
(a) small cubes can be cut in half
(b) an extra layer of 9x10=90 cubes is added, completely filling the prism (and sticking out over the top)
To find out how many small cubes are needed to completely fill the rectangular prism, we can start by calculating the volume of the rectangular prism.
The length of the rectangular prism is 4 1/2 inches, which can be written as a mixed fraction: 4 + 1/2 = 9/2 inches.
The width of the rectangular prism is 5 inches.
The height of the rectangular prism is 3 3/4 inches, which can be written as a mixed fraction: 3 + 3/4 = 15/4 inches.
To calculate the volume of the rectangular prism, we multiply the length, width, and height together:
Volume = Length × Width × Height
Volume = (9/2) inches × 5 inches × (15/4) inches
Now, simplify the fractions:
Volume = (9/2) × 5 × (15/4)
Volume = (9 × 5 × 15) / (2 × 4)
Volume = (675) / (8)
Volume = 84.375 cubic inches
Since the edge length of each small cube is 1/2 inch, we need to find out how many small cubes can fit into the volume of the rectangular prism.
To calculate that, divide the volume of the rectangular prism by the volume of each small cube:
Number of small cubes = Volume of the rectangular prism / Volume of each small cube
Number of small cubes = 84.375 cubic inches / (1/2 inch)^3
Now, cube the denominator:
Number of small cubes = 84.375 cubic inches / (1/8) cubic inches
Divide the numerator by the reciprocal of the denominator:
Number of small cubes = 84.375 cubic inches × 8 cubic inches
Number of small cubes = 675
Therefore, you would need 675 small cubes to completely fill the rectangular prism.