Answer
$P = 315~W$
Work Step by Step
We can find the temperature of the sphere:
$\lambda = \frac{2.9\times 10^6~nm~K}{T}$
$T = \frac{2.9\times 10^6~nm~K}{\lambda}$
$T = \frac{2.9\times 10^{-3}~m~K}{2.0\times 10^{-6}~m}$
$T = 1450~K$
We can find the power emitted by the sphere:
$P = e~\sigma~A~T^4$
$P = (1)~(5.67\times 10^{-8}~W~m^{-2}~K^{-4})(4\pi)(1.0\times 10^{-2}~m)^2~(1450~K)^4$
$P = 315~W$