Given:
ab tangent at d, ad = od = 4
find: area of the shaded region

AB tangent at D, AD = OD = 4
so triangle OAD is right angle with side of 4 and 4.
area of OAD = 1/2 * 4 * 4 = 8

Angle AOD = DAO = 45 deg.
so circular sector OCD area = area of circle O * 45/360
= pi * 4 * 4 * 45/360
= 2pi

Shade area ACD = trigangle OAD - circular sector OCD
= 8 - 2pi
= 1.72

Hello!
volume of sphere =4/3.pi.r^3