#### Answer

Men's basketball: 10in boxes
Youth basketball: 9in boxes

#### Work Step by Step

Men's Basketball:
use:
$C=\pi d$
$29.5=\pi d$
$d=\frac{29.5}{\pi}\approx9.39$
Youth basketball:
use:
$C=\pi d$
$27.75=\pi d$
$d=\frac{27.75}{\pi}\approx8.83$
$8\lt9\lt9.39\lt10$ The diameter of the men's basketball is greater than 8 and 9 inches but less than 10 inches which means that the smallest box those balls can fit in is this one with a 10-inch long edge.
$8\lt8.83\lt9\lt10$. The diameter of the men's basketball is greater than 8 inches but less than 9 and 10 inches which means that the smallest box those balls can fit in is this one with a 9-inch long edge.