A cube is inscribed in a hemisphere of radius R , such that four of its vertices lie on the - Maths - Surface Areas and Volumes

Question

A cube is inscribed in a hemisphere of radius R , such that four
of its vertices lie on the base of the hemisphere and the other
four touch the hemispherical surface of the sphere of the sphere
Find the volume of cube

Priyanka Kedia · Accepted Answer

Let a be the side of cube ABCDEFGH and O be the centre of the hemisphere Then, OA = OC =R Diagonal of cube AC = âˆš2 a Let P be the mid-point of AC OP = a

Now, in âˆ† AOP,

A cube is inscribed in a hemisphere of radius R , such that four of its vertices lie on the base of the hemisphere and the other four touch the hemispherical surface of the sphere of the sphere. Find the volume of cube.