Question

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.

Answer 1

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