The diagonal of the axial section of the cylinder forms an angle of 45 degrees

The diagonal of the axial section of the cylinder forms an angle of 45 degrees with the base plane. Find the height of the cylinder if the radius of its base is 6 cm.

A cylinder is a geometric body formed by rotating a rectangle around one of its sides.

The axial section of a cylinder is a plane passing through the center of its bases. The diagonal of the axial section of the cylinder, its diameter and height form a right-angled triangle. Thus, to calculate the height, you can use the tangent of the angle formed by the diagonal of the axial section and the base. The tangent of an acute angle of a right-angled triangle is the ratio of the opposite leg to the adjacent one:

tg α = H / D;

H = D * tg α, where:

H – height;

D is the base diameter;

α is the angle between the diagonal and the base;

tg 45º = 1;

D = 2R;

D = 2 * 6 = 12 cm;

H = 12 * 1 = 12 cm.

Answer: The height of the cylinder is 12 cm.