Question

A right rectangular prism's edge lengths are 4 1 2 inches, 4 inches, and 3 inches. How many unit cubes with edge lengths of 1 3 inch can fit inside the prism?

Answer 1

Question:

A right rectangular prism's edge lengths are
`4(1)/(2)` inches, 4 inches, and 3 inches. How many unit cubes with edge lengths of
`(1)/(3)` inch can fit inside the prism?

Answer:

1458 cubes with edge lengths of
`(1)/(3)` inch can fit inside the prism.

Explanation:

Given:

Dimensions of the rectangular prism =
`4(1)/(2)` inches, 4 inches, and 3 inches

length of Edge of the cube =
`(1)/(3)`

To Find:

Number of unit cubes that can fit inside the prism =?

Solution:

Step 1: Finding the volume of the right rectangular prism

Volume of the right Rectangular prism is =
`w* h* l`

where

w = width of theright Rectangular prism

h = height of the right Rectangular prism

l = lenght of the right Rectangular prism

Substituting the values ,

Volume of the right Rectangular prism is =
`4(1)/(2)*4* 3`

Volume of the right Rectangular prism is =
`(9)/(2)*4* 3`

Volume of the right Rectangular prism is =
`4.5*4* 3`

Volume of the right Rectangular prism is = 54
`inch^3`

Step 2: Finding the volume of the cube

Volume of the cube =
`(edge)^3`

Substituting the values,

Volume of the cube =
`( (1)/(3))^3`

Volume of the cube =
`( (1)/(27))`

Step 3: Find the number of cube that can fit in the cube.

Number of cubes =
`\frac{\text{volume of the right Rectangular prism}}{\text{Volume of the cube}}`

Number of cubes =
`(54)/((1)/(27))`

Number of cubes =
`54*27`

Number of cubes = 1458 cubes