A cylindrical hole of radius 1 is bored through a solid ball of radius 2. Find the volume and outer surface area.

Outer surface area = outer surface area of the cylindrical ball - surfase area of the two circle top and bottom of the cylindrical hole = 4πr^2 - 2 (πR^2) = 4π (2) ^2 - 2 (π (1) ^2) = 16π - 2π = 43.98 square units

Volume = 4/3 (πr^3) - πR^2h; where h is the height of the cylinder given by 2 (r - sqrt (r^2 - R^2))

V = 4/3π (2) ^3 - π (1) ^2 (2 (2 - sqrt (2^2 - 1^2))) = 4/3π (8) - π (2 (2 - sqrt (4 - 1))) = 32/3π - π (2 (2 - sqrt (3))) = 32/3π - π (4 - 2sqrt (3)) = 31.83 cubic units.