Answer
(a) $V = 864~m^3$
(b) $V = 691.2~m^3$
Work Step by Step
(a) We can find the volume Tracy measures for the barn:
$V = 16~m \times 4.5~m \times 12~m$
$V = 864~m^3$
(b) Let $L_0 = 16~m$. We can find the length $L$ that Octavio measures for the barn:
$L = \frac{L_0}{\gamma}$
$L = L_0~\sqrt{1-\frac{v^2}{c^2}}$
$L = (16~m)~\sqrt{1-\frac{(0.60~c)^2}{c^2}}$
$L = (16~m)~\sqrt{1-0.36}$
$L =12.8~m$
Since the height and depth of the barn are perpendicular to the direction of motion, they do not have any length contraction. We can find the volume Octavio measures for the barn:
$V = 12.8~m \times 4.5~m \times 12~m$
$V = 691.2~m^3$
