# A cone with a generatrix equal to 13 is inscribed in a cylinder with a base diameter equal to 10.

September 14, 2021 | education

| **A cone with a generatrix equal to 13 is inscribed in a cylinder with a base diameter equal to 10. Find the height of the cylinder.**

The base of the cone is parallel to the top base of the cylinder, then AO is parallel to BD. The height of the OB cone is parallel to the height of the AD cylinder, then ADBO is a rectangle, BD = AO = AC / 2 = 10/2 = 5 cm.

In a right-angled triangle ADB, according to the Pythagorean theorem, we determine the length of the leg AD.

AD ^ 2 = AB ^ 2 – BD ^ 2 = 169 – 25 = 144.

AD = 12 cm.

Answer: The height of the cylinder is 12 cm.

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