The radius of the base of the cone is 20. Through the middle of the height of the cone

univerkov | May 3, 2021 | education

The radius of the base of the cone is 20. Through the middle of the height of the cone, a plane is drawn parallel to the base. Then the cross-sectional area is equal to.

A section parallel to the base is a circle.

The area of the circle is found by the formula: S = 2nR².

Let A – the top of the cone, AO – the height of the cone, AB – the radius of the base, AB = 20, point O1 – the midpoint of the height AO. О1В1 – section radius.

Consider triangles AOB and AO1B1: angle A is common, angle O is equal to angle O1 (= 90 °). This means that triangles are similar in two angles. Since O1 is the middle of AO, the similarity coefficient is:

k = AO / AO1 = 2. Hence, OB / O1B1 = 2, hence O1B1 = 10.

Find the cross-sectional area: S = 2 * n * 10 = 20n.

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.