Problem: The volume of a rectangular solid each of whose side, front, and bottom faces are 12 sq. in., 8 sq. in., and 6 sq. in. respectively is:
Answer Choices:
A. 576 cu.in.
B. 24 cu.in.
C. 9 cu.in.
D. 104 cu.in.
E. none of the above answers
Solution:
lh=12,hw=8 and lw=6. Eliminating h we obtain l=3w/2. Eliminating l,3w2/2=6.∴w=2,l=3,h=4, and
V=lwh=24;
or
V2=(lwh)2=lh⋅hw⋅lw=12⋅8⋅6=42⋅62.∴V=4⋅6=24.