Question

A right rectangular prism is packed with cubes of side length Fraction 1 over 3 inch. If the prism is packed with 6 cubes along the length, 4 cubes along the width, and 8 cubes along the height, what is the volume of the prism?

Fraction 7 and 1 over 9 cubic inches

Fraction 17 and 7 over 9 cubic inches

16 cubic inches

192 cubic inches

Answer 1

The correct answer is :7 and 1 over 9 cubic inches that is
`7(1)/(9) inches^3`.

Explanation:

Length of the cube = a =
`(1)/(3) inch`

Volume of the cube = V

V=
`a^3` =
`((1)/(3) inch)^3=(1)/(27) inch^3`

Right rectangular prism is packed with these cubes:

Number of cubes placed along the length = 6 cubes

Number of cubes placed along the width = 4 cubes

Number of cubes placed along the height = 8 cubes

Total number of cubes in the right rectangular prism = 6 × 4 × 8 = 192 cubes

Volume of the right rectangular prism :

Number of cubes × Volume of cube

`= 192* (1)/(27) inch^3=7(1)/(9) inches^3`

Answer 2

Length of prism = 1/3 x 6 = 2 inches
Width of prism = 1/3 x 4 = 4/3 inches
Height of prism = 1/3 x 8 = 8/3 inches

Volume of prism = 2 x 4/3 x 8/3 = 7 1/9 cubic inches