A cylinder is inscribed in the cone so that its upper base touches the lateral surface of the cone

| February 26, 2021 | education

A cylinder is inscribed in the cone so that its upper base touches the lateral surface of the cone, and the lower one lies in the plane of its base. Find the area of the lateral surface of a cylinder if the height of the cone is 10 root of 3 cm, the height of the cylinder is 4 root of 3 cm, and the generatrix is inclined to the base plane at an angle of 60 °

According to the condition, the height of the cone OС = 10 * √3 cm, and the height of the cylinder OO1 = 4 * √3 cm, then the segment O1C = OС – OO1 = 10 * √3 – 4 * √3 = 6 * √3 cm.

Triangles AOC and BO1C are rectangular and similar in acute angle C, then the angle OAC = O1BC = 60. In a right-angled triangle O1BC, we determine the length of the leg O1B.

tgO1BC = О1С / О1В, then О1В = О1С / tg60 = 6 * √3 / √3 = 6 cm.

Let us determine the area of the lateral surface of the cylinder.

Side = 2 * n * O1B * OO1 = 2 * n * 6 * 4 * √3 = n * 48 * √3 cm2.

Answer: The area of the lateral surface of the cylinder is n * 48 * √3 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.