The volume of the cone is 250. Through the point dividing the height of the cone in a ratio of 3: 2, counting from the top

| April 30, 2021 | education

The volume of the cone is 250. Through the point dividing the height of the cone in a ratio of 3: 2, counting from the top, parallel to the base of the cone, a section is drawn, which is the base of a smaller cone with the same apex. Find the volume of the smaller cone.

The large and cut off cones are similar figures, since their bases are parallel, the heights and generators lie on the same straight lines.

Let the length of the segment O2 = 3 * X cm, then, by condition, the length of the segment O1O2 = 2 * X cm.

Height length OO1 = OO2 + O1O2 = 3 * X + 2 * X = 5 * X.

Then the coefficient of similarity of the cones is: K = OO1 / O1O2 = 5 * X / 3 * X = 5/3.

The volumes of such figures are referred to as a cube of the coefficient of their similarity.

V1 / V2 = (5/3) 3 = 125/27.

V2 = V1 * 27/125 = 250 * 27/125 = 2 * 27 = 54 cm3.

Answer: The volume of the cut off cone is 54 cm3.



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.