Some really wet-finger math: a cone is one third the volume of a cylinder with the same base and height. That means you could build the mountain 3 times as high

Some really wet-finger math: a cone is one third the volume of a cylinder with the same base and height. That means you could build the mountain 3 times as high as the tower for same weight. So you can get a 10.5km high mountain. Assuming, ofcourse, the weight is perfectly distributed over the entire base area. So, we can just about build Mauna Kea with bricks.