Final answer:
To determine how many small cubes can fit in the rectangular prism, calculate the volume of the prism and cube in inches and divide the prism's volume by the cube's volume. The result is that 7727 small cubes can be packed into the rectangular prism.
Step-by-step explanation:
To determine how many small cubes can be packed in the rectangular prism, we first need to calculate the volume of both the rectangular prism and the small cube. The dimensions of the rectangular prism are 1 and 1 over 3 feet (which equals 4/3 feet) by 1 foot by 2 and 1 over 3 feet (which equals 7/3 feet). Convert these dimensions to inches because the small cube is measured in centimeters which are closer in scale to inches and the calculation requires the same units. The conversion for feet to inches is 1 foot = 12 inches.
Rectangular prism dimensions in inches:
Length: 4/3 feet * 12 inches/foot = 16 inches
Width: 1 foot * 12 inches/foot = 12 inches
Height: 7/3 feet * 12 inches/foot = 28 inches
Next, calculate the volume of the rectangular prism:
Volume of prism = Length * Width * Height
Volume of prism = 16 inches * 12 inches * 28 inches
Volume of prism = 5376 cubic inches
We must then convert the dimensions of the small cube to inches:
Small cube dimensions in inches:
1.80 cm * 0.393701 inches/cm = 0.708662 inches
2.05 cm * 0.393701 inches/cm = 0.807487 inches
3.10 cm * 0.393701 inches/cm = 1.220373 inches
Next, calculate the volume of the small cube:
Volume of cube = Length * Width * Height
Volume of cube = 0.708662 inches * 0.807487 inches * 1.220373 inches
Volume of cube ≈ 0.696 cubic inches
To find out how many small cubes can fit inside the rectangular prism, divide the volume of the prism by the volume of the cube:
Number of small cubes = Volume of prism / Volume of cube
Number of small cubes = 5376 cubic inches / 0.696 cubic inches
Number of small cubes ≈ 7727
Therefore, 7727 small cubes can be packed into the rectangular prism.