A right rectangular prism has these dimensions:Length: Fraction 1 and 1 over 2 unitsWidth: Fraction 1 over 2 unitHeight: Fraction 3 over 4 unitHow many cubes of side length Fraction 1 over 4 unit are required to completely pack the prism without any gap or overlap? 36 45 51 60

Hey there :)

The volume formula of a rectangular prism is
V = height x length x width

Given are:
Length = [tex] 1\frac{1}{2} = \frac{3}{2} [/tex]
Width = [tex] \frac{1}{2} [/tex]
Height = [tex] \frac{3}{4} [/tex]

Lets find the volume:
V = [tex] \frac{3}{2} [/tex] x [tex] \frac{1}{2} [/tex] x [tex] \frac{3}{4} [/tex]
   =  [tex] \frac{9}{16} [/tex] units³

The volume formula of a cube is
V = side³

Given is:
Side = [tex]( \frac{1}{4} )^3[/tex]  
        = [tex] \frac{1}{64} [/tex] units³

To find how many cubes fit in the rectangular prism, we divide the volumes
Volume of prism divided by volume of cube
[tex] \frac{9}{16} [/tex] ÷ [tex] \frac{1}{64} [/tex]
Since it is a fraction that is involved in division, we find the reciprocal and multiply

= [tex] \frac{9}{16} [/tex]  x  64 
= 36

Your answer will be the 1st option