Answer
$I = 0.193~kg~m/s$
Work Step by Step
Let $m_r$ be the mass along the rim and let $m_s$ be the mass of one spoke.
$I = m_r~r^2 + (8\times \frac{1}{3}m_s~r^2)$
$I = (1.40~kg)(0.300~m)^2 + (8\times \frac{1}{3}(0.280~kg)(0.300~m)^2)$
$I = 0.193~kg~m/s$
