Steiner’s theorem and gyration radius. A metal tank wheel in the shape of a disc of radius R is lightened by cutting out six identical through- holes in the shape of discs, whose axes are parallel to the wheel’s axis of rotation, and whose radii are all r. The holes’ centers are positioned at the vertices of a regular hexagon of side A, with the wheel’s axis passing through the center of the hexagon. a) By what percentage is the wheel lightened, as a result of the cutouts, for r=R/5?

Steiner’s theorem and gyration radius. A metal tank wheel in the shape of a disc of radius R is lightened by cutting out six identical through- holes in the shape of discs, whose axes are parallel to the wheel’s axis of rotation, and whose radii are all r. The holes’ centers are positioned at the vertices of a regular hexagon of side A, with the wheel’s axis passing through the center of the hexagon. a) By what percentage is the wheel lightened, as a result of the cutouts, for r=R/5?