The generatrix of the cone is 15 cm, the radius of its base is 12 cm. A section is drawn through its apex and a chord

| August 10, 2021 | education

The generatrix of the cone is 15 cm, the radius of its base is 12 cm. A section is drawn through its apex and a chord of the base equal to 18 cm. Find the height of the cone, the cross-sectional area.

The height of the cone is determined from the right-angled triangle AOB in which AO = R = 12 cm, AB = 15 cm.

OB ^ 2 = AB ^ 2 – AO ^ 2 = 255 – 144 = 81.

OB = 9 cm.

The section of the ВKM is an isosceles triangle, ВK = ВM = 15 cm.

We will construct the median and the height of the BH, then KH = KM / 2 = 18/2 = 9 cm.By the Pythagorean theorem, in a right-angled triangle BHK, BH ^ 2 = AK ^ 2 – KH ^ 2 = 225 – 81 = 144.

BH = 12 cm.

Determine the cross-sectional area. Ssection = KM * ВН / 2 = 19 * 12/2 = 108 cm2.

Answer: The height of the cone is 9 cm, the cross-sectional area is 108 cm2.



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