Answer:
810 cubes
Step-by-step explanation:
step 1
Find the volume of the rectangular prism
The volume of the rectangular prism is
[tex]V=LWH[/tex]
we have
[tex]L=2\frac{1}{2}\ in=2+\frac{1}{2}=\frac{5}{2}\ in[/tex]
[tex]W=2\ in\\H=6\ in[/tex]
substitute
[tex]V=(\frac{5}{2})(2)(6)[/tex]
[tex]V=30\ in^3[/tex]
step 2
Find the volume of the cube
The volume of the cube is
[tex]V=b^3[/tex]
where
b is the length side of the cube
we have
[tex]b=\frac{1}{3}\ in[/tex]
substitute
[tex]V=(\frac{1}{3})^3[/tex]
[tex]V=\frac{1}{27}\ in^3[/tex]
step 3
Find out how many unit cubes with edge lengths of 1/3 inch can fit inside the prism
Divide the volume of the prism by the volume of the cube
[tex]30:\frac{1}{27}=30(27)=810\ cubes[/tex]
