# The height of the cone is 5 and the diameter of the base is 24. Find the generatrix of the cone.

August 25, 2021 | education

| The radius of the base of the cone, its apothem and height form a right-angled triangle BOC.

The radius of the circle at the base of the cone is: R = OB = AB / 2 = 24/2 = 12 cm.

Then, by the Pythagorean theorem, we determine the length of the BC hypotenuse.

ВС ^ 2 = OC ^ 2 + ОВ ^ 2 = 5 ^ 2 + 12 ^ 2 = 25 + 144 = 169.

BC = 13 cm.

The hypotenuse BC is the generatrix of the cone.

Answer: The generatrix of the cone is 13 cm.

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