The following was given as an intuitive explanation of understanding why a sphere's area is four times the area of the flat circle sharing a perimeter with a greater circle on the sphere. I don't understand spatially how the cylinder and sphere are oriented. Please help. Let Z be a cylinder of height 2r touching the sphere Sr along the equator θ=0. Consider now a thin plate orthogonal to the z-axis having a thickness Δz≪r. It intersects Sr at a certain geographical latitude θ in a nonplanar annulus of radius ρ=rcosθ and width Δs=Δz/cosθ, and it intersects Z in a cylinder of height Δz. Both these "annuli" have the same area 2πrΔz. As this is true for any such plate it follows that the total area of the sphere Sr is the same as the total area of Z, namely 4πr2.