A cube whose side is 8 meters is inscribed in a sphere. Compute the area of the lune of the sphere if the central angle is 45 degrees.
Area of lune of a sphere is A = 2ΘR^2,
Where Θ = π/4 rad.
Diagonal of cube = diagonal of sphere = 2R
Cube diagonal is 2R = √(8^2 + 8^2 + 8^2) = 8√(3)
R = 4√(3)
A = 2ΘR^2 = 2*(π/4)*16*3 = 8π*3
A = 24π sq metres