Solution
= Solution
The <sphere> has surface area $4\pi R^2=400\pi\,\mathrm{m^2}$. Dividing the given surface-patch area by that total gives the dimensionless fraction
$$
\boxed{\frac{10}{400\pi}=\frac1{40\pi}\approx0.00796,}
$$
or about \b[$0.796\%$] of the surface. The patch area is already measured on the surface, so no planar projection or spherical-cap conversion is needed.