Find the volume of a body of revolution obtained by rotating a right-angled triangle with a hypotenuse of 18 cm

Find the volume of a body of revolution obtained by rotating a right-angled triangle with a hypotenuse of 18 cm. and an acute angle of 15 degrees around one of the legs.

The figure formed as a result of rotation of a right-angled triangle about the leg is a cone, the generatrix of which is the hypotenuse of the triangle, and the legs are the radius of the circle and the height.

In a right-angled triangle ABO, AO = R = AB * Sin15 = 18 * 0.256 = 4.66 cm.

BО = AB * Cos15 = 18 * 0.966 = 17.39 cm.

Determine the volume of the cone.

V = π * R ^ 2 * BO / 3 = π * 4.662 * 17.39 / 3 = π * = 427.2 cm3.

If the axis of rotation is the smaller leg, then AO = R = 17.39 cm, BO = 4.66 cm.

Then V = 1475 cm3.

Answer: The volume of the cone is 427.2 cm3, or 1475 cm3.