A section is drawn through the apex of the cone at an angle of 30 degrees to its height.

| April 24, 2021 | education

A section is drawn through the apex of the cone at an angle of 30 degrees to its height. Find the cross-sectional area if the height of the cone is 3√3 cm and the radius is 5 cm.

In a right-angled triangle BOH, we determine the length of the leg OH.

tg30 = OH / OB.

OH = ОВ * tg30 = 3 * √3 / √3 = 3 cm.

The IOC triangle is isosceles, since OK = OM = R, and the OH height is its median, then HK = HM = KM / 2.

By the Pythagorean theorem, we determine the length of the leg HK.

HK ^ 2 = OK ^ 2 – OH ^ 2 = 25 – 9 = 16.

HK = 4 cm, then MK = 2 * HK = 2 * 4 = 8 cm.

In a right-angled triangle BH, we determine the length of the hypotenuse BH. The OH leg lies opposite the angle 30, then its length is equal to half the length of BH. OH = BH / 2.

BH = 2 * OH = 2 * 3 = 6 cm.

Determine the cross-sectional area.

Svkm = MK * BH / 2 = 8 * 6/2 = 24 cm2.

Answer: The cross-sectional area is 24 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.