Given a cylinder, a cone is inscribed in it, find the volume of the cone, the volume of the cylinder is 135.

We write down the formulas for the volumes of the cylinder and the cone, respectively: Vc = S * h and Vk = 1/3 S * h, where S is the area of the base of the cylinder and cone, h is the height of the cylinder and cone.

And so, as can be seen from the formulas, the volume of the cylinder is 3 times greater than the volume of the cone or the volume of the cone is 3 times less than the volume of the cylinder, that is, V c / V k = (S * h) / (1/3 S * h) = 3.

From the condition of the problem, we know that Vc = 135, which means Vk = Vts / 3 = 135/3 = 45.

Answer: 45.