The dimensions of a rectangular prism are shown below: 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? 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.

A - 30 cubes

B - Volume of prism = feet³

Step-by-step explanation:

We are given that the dimensions of the rectangualr prism is,

Length = = feet

Width = 1 foot

Height = = feet

Thus, the volume of the prism = Length × Width × Height

i.e. Volume of the prism = × 1 × = feet³

Now, the side of the cube = foot each.

Volume of the cube = = feet³

Part A: Number of cubes which can be packed inside the prism are given by,

Number of cubes = Volume of prism divided by Volume of cube

i.e. Number of cubes =

i.e. Number of cubes =

i.e. Number of cubes = 15 × 2 = 30

Hence, 30 cubes can be packed inside the rectangular prism.

Part B: As we have, there are 30 cubes which can be fit inside the prism.

Since, the volume of 1 cube = feet³

So, Volume of 30 cube = = feet³

Thus, the volume of the rectangular prism is feet³.

Dimensions of a rectangular prism

Length

      foot

Breadth

   =1 foot

Height

   foot

Volume of Rectangular prism

            =Length × Breadth × Height

Dimension of Cube is

Each side Length is .

Volume of Cube is

                 =Side × Side ×Side

Part A

Number of Small cubes which can be fitted inside a Rectangular Prism

Part B

⇒Volume of Rectangular prism=30 × Volume of  cube having dimension .

→Volume of cube having side length 1 foot

=1×1×1

=1 cubic foot

⇒Volume of Rectangular prism=× Volume of  cube having side of length 1 unit.                              

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step-by-step explanation: