The height of the smaller box is 80% of the height of the larger box, while the other two dimensions are the same for both boxes. what is the difference in the volume of these two boxes? the height of the smaller box is 12in , width 2in ,and length 7 3/4.

Let
z> the height of the larger box
x> the length side of the box (smaller and larger box)
y> the width side of the box (smaller and larger box)

volume larger box=x*y*z
volume smaller box=x*y*(0.80z)> 0.80[x*y*z]

the difference in the volume of these two boxes=[x*y*z]*(1-0.80)
the difference in the volume of these two boxes=0.20*[x*y*z]

The height of the smaller box is 12 in
so 
z*0.8=12> z=12/0.8> z=15 in
x=7 3/4 in> (7*4+3)/4> 31/4 in
y= 2 in

the difference in the volume of these two boxes=0.20*[(31/4)*2*15]
the difference in the volume of these two boxes=46.5 in³

the answer is
46.5 in³

The first option would be correct if it were one half and not one