Length: 1 and 1 over 2feet
Width: 1 foot
Height: 2 and 1 over 2feet
The lengths of the sides of a small cube are 1 over 2 foot each.
Part A: How many small cubes can be packed in the rectangular prism
To find the number of small cubes that can be packed in the rectangular prism, we need to calculate the volume of both the small cube and the rectangular prism.
The volume of a rectangular prism can be calculated by multiplying its length, width, and height. In this case, the length is 1 and 1 over 2 feet, the width is 1 foot, and the height is 2 and 1 over 2 feet.
Volume of the rectangular prism = (1 and 1 over 2) ft × 1 ft × (2 and 1 over 2) ft
To calculate this volume, we need to convert the mixed numbers into improper fractions.
1 and 1 over 2 = 3/2
2 and 1 over 2 = 5/2
Volume of the rectangular prism = (3/2) ft × 1 ft × (5/2) ft
Next, we can calculate the volume of the small cube. Since all sides of the small cube have a length of 1 over 2 foot, its volume is simply (1/2) ft × (1/2) ft × (1/2) ft.
Now we can compare the volume of the rectangular prism to the volume of the small cube to determine how many small cubes can be packed inside.
To do this, we divide the volume of the rectangular prism by the volume of the small cube:
Number of small cubes = Volume of rectangular prism / Volume of small cube
Substituting the values:
Number of small cubes = [(3/2) ft × 1 ft × (5/2) ft] / [(1/2) ft × (1/2) ft × (1/2) ft]
The units of feet will cancel out, and we will be left with the number of small cubes that can be packed inside the rectangular prism.