Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / 6 / a

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 fractionor about $0.796\%$ of the surface. The patch area is already measured on the surface, so no planar projection or spherical-cap conversion is needed.