The axial section of the cone is an isosceles triangle, the angle at the base of which

| June 10, 2021 | education

The axial section of the cone is an isosceles triangle, the angle at the base of which is 30 degrees, and the base is 8 dm. Find the volume of the cone.

1. The base of an isosceles triangle, which is the axial section of the cone, is the diameter of the base of the cone. Find the radius:

r = d / 2 = 4 (dm).

2. The volume of the cone is found by the formula V = 1 / 3Sb * h, where Sb is the area of ​​the base. Find Sbase:

Sb = nr ^ 2 = 3.14 * 4 ^ 2 = 50.24 (dm2).

3. Find the height of the cone “h”, that is, the height of the isosceles triangle, which is the section of the cone. The height divides the triangle into 2 right-angled triangles. Knowing that the angle at the base is 30º and the adjacent leg, which is the radius of the base, is equal to 4 dm, we calculate:

h = tg 30º * 4 = (4√3) / 3 (dm).

4. Find the volume:

V = 1/3 * 50.24 * (4√3) / 3 = 22.33√3 = 38.67 (dm3).

Answer: cone volume = 38.67 (dm3).



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.