The radii of the bases of the truncated cone are 3 and 6 cm, and the height is 4 cm.

| April 27, 2021 | education

The radii of the bases of the truncated cone are 3 and 6 cm, and the height is 4 cm. find the area of the axial section and the lateral surface of the cone.

The height BH divides the radius OA into segments AH and OH.

Since BO1ON is a quadrangle, OH = BO1 = 3 cm.

Then AH = AO – OH = 6 – 3 = 3 cm.

In a right-angled triangle ABN, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = BH ^ 2 + AH ^ 2 = 16 + 9 = 25.

AB = 5 cm.

The axial section of the truncated pyramid is an isosceles trapezoid, the bases of which are the diameters of the circles.

BC = BO1 * 2 = 3 * 2 = 6 cm.

AD = AO * 2 = 6 * 2 = 12 cm.

Determine the area of ​​the axial section.

Ssection = (ВС + АD) * ВН / 2 = (6 + 12) * 4/2 = 36 cm2.

Let us determine the area of ​​the lateral surface of the cone.

Side = n * (BO1 + AO) * AB = n * (3 + 6) * 5 = n * 45 cm2.

Answer: The axial section area is 36 cm2, the lateral surface area is n * 45 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.