Answer
$1.4\times10^3\frac{decays/s}{m^{2}}$
Work Step by Step
Use the surface area of a sphere, $4 \pi r^2$ and find the activity per square meter.
$$\frac{Activity}{m^2}=\frac{2.0\times10^7Ci}{4\pi r^{2}_{Earth}}$$
$$=\frac{(2.0\times10^7Ci)(3.7\times10^{10}decays/s)}{4\pi (6.38\times10^6 m)^{2}}$$
$$=1.4\times10^3\frac{decays/s}{m^{2}}$$