Calculate the height of the cone if its generatrix is 17 cm, and the diameter of the base is 16 cm.

univerkov | August 6, 2021 | education

Point B of the height of the cone is projected to point O, the center of the circle. The OB height is perpendicular to the plane of the cone base.

Then the triangle BOC is rectangular in which the hypotenuse is the generatrix of the cone, OC is the radius of the circle at the base of the cone.

OC = AC / 2 = 16/2 = 8 cm.

By the Pythagorean theorem, OB ^ 2 = BC ^ 2 – OC ^ 2 = 17 ^ 2 – 8 ^ 2 = 289 – 64 = 225.

ОВ = h = 15 cm.

Answer: The height of the cone is 15 cm.

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