Answer
$r=8.3\times 10^{10}m$
Work Step by Step
We know that
$T^2=\frac{4\pi^2}{GM_S}r^3$
This can be rearranged as:
$r=\sqrt[3] {\frac{GM_ST^2}{4\pi^2}}$
We plug in the known values to obtain:
$r=\sqrt[3] {\frac{(6.67\times 10^{-11})(2.00\times 10^{30})(1.3\times 10^7)^2}{4\pi^2}}$
$r=8.3\times 10^{10}m=0.55A.U$
