Question

The volume of a rectangular solid each of whose side, front and bottom faces are 12 sq.cm., 8 sq. cm., and 6 sq. cm. respectively, is:

• A. 576 cu. cm.
• B. 24 cu. cm.
• C. 9 cu. cm.
• D. 104 cu. cm.
• E. None of these

Answer 1

The correct option is B 24 cu. cm.

$lh=12$, $hw=8$ and $lw=6$. Eliminating $h$ we obtain $l=\frac{3w}{2}.$
Eliminating $l$, $\frac{3w^2}{2}=6$. $\therefore$ $w=2$, $l=3$, $h=4$, and $V=lwh=24$;
Or $V^2=(lwh{)}^2=lh.hw.lw=12.8.6=4^2.6^2$
$\therefore$ $V=4.6=24$