Assume point $A$ is a light source that emits light into a cone, as shown in the diagram below, and illuminates a circular surface with a distance $d$ from the light source and a radius $r.$

a$)$ Given $d=5ft$ and $r=8\mathrm{.}66ft,$ calculate the solid angle subtended by this surface to the point A

b$)$ If the luminous flux from point $A$ is $100$ Im $,$ calculate the luminous intensity in the direction of this solid angle.

c$)d=10ft$ and $r=0\mathrm{.}1ft,$ calculate the solid angle of this surface to the point A by using two methods $-$ approximate method and exact method