I am giving a Brainliest to the best!

A right rectangular prism has these dimensions:

Length: 1 and 1/3 units

Width: 5/6 unit

Height: 2/3 unit

How many cubes of side length 1/6 unit are required to completely pack the prism without any gap or overlap?

A 40

B 80

C 160

D 240

Ok so find the total volume and find how many volumes of cubes will fit

find

a. volume of prism

b. volume of 1 cube

a. LWH=A

1 and 1/3=4/3, note

so

LWH = (4/3) (5/6) (2/3) = 40/54=20/27 cubic units

b. volume of cube=side^3

side=1/6

vcube = (1/6) ^3=1/216

so

how many cubes fit into the big container?

1/216 times n=20/27

times both sides by 216/1

n=4320/27

n=160

160 of them fit

C is answer

To find the number of 1/6 unit cubes, you have to convert all the dimensions into 6ths. 1 1/3 converts into 8/6 and 2/3 converts into 4/6 if you multiply both by 2/2, which is equal to 1. Next, you multiply all the dimensions together, because to find volume, you have to use this formula: base times height times width = V (volume). 8/6 times 4/6 gives you 32/36, and 32/36 times 5/6 gives you 160/216 units³. Then, you have to find the volume of the 1/6 cube. 1/6 times 1/6 times 1/6 = 1/216 units³. Finally, you divide 160/216 by 1/216, and there are 160 1/216 in 160/216, so the answer is "C," 160 1/6 side length cubes can fit into the rectangular prism without any gap or overlap.