The dimensions of a rectangular prism are shown below: length: 2 and 1 over 4 feet width: 1 foot height: 1 and 1 over 4 feet the lengths of the sides of a small cube are 1 over 4 foot each. part a: how many small cubes can be packed in the rectangular prism? show your work. (5 points) part b: use the answer obtained in part a to find the volume of the rectangular prism in terms of the small cube and a unit cube. (5 points)

Step-by-step explanation:

Part A: The length of the prism is = feet

Width = 1 foot

Height = feet

So, volume of the prism = length x width x height

V = = cubic feet.

The lengths of the sides of a small cube are = foot

Volume of cube = side x side x side

V = = cubic foot

Number of small cubes that can be packed in the prism =

=

= = 180 cubes

Hence, 180 cubes can be packed into rectangular prism.

Part B: Unit cube volume is 1x1x1 =1 cubic foot

So, 180 cubes will have 180 cubic foot volume.

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