Iam giving a brainliest to the
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

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.

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

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