Answer
.2063
Work Step by Step
We know that the moment of inertia must decrease by 70 percent, so we multiply the current moment of inertia by .7. In addition, we know that the wheel must go down in diameter from .38 to .35, so we multiply by $\frac{.35}{.38}$. Thus, we find:
$I_{new}=.32 \times .7 \times \frac{.35}{.38}=\fbox{.2063}$
