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. (5 points)

Step-by-step explanation:                    

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 =

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

20

step-by-step explanation:

27/4x^6 y^8

step-by-step explanation:

4(3x^2y^4)^3 (2x^3y^5)^4

=

108x^6 y^12 /16x^12 y^20

=

108 /16x^6 y^8

=

27 /4x^6 y^8