Solid Angle of Cylindrical Detector and Intrinsic Peak Efficiency

Find the solid angle subtended by the circular end surface of a cylindrical detector
(diameter of 10 cm) for a point source located 20 cm from the surface along the
cylindrical axis.

Also, assume that this detector has an intrinsic peak efficiency at 1 MeV of 12%. The
point source emits a 1 MeV gamma ray in 80% of its decays and has an activity of 20
kBq. Neglecting attenuation between the source and detector, calculate the number of
counts that will appear under the 1 MeV full-energy peak in the pulse height spectrum
from the detector over a 100 s count.

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