Some water towers are composite shapes of a cylinder with a cone on top. One such tower is 8 ft. off the ground, and the cylinder is 6 ft. tall with a diameter of 6 ft. The slant height of the cone is 4 ft. Find the height of the tower from the ground to the vertex of the cone. Round the answer to the nearest tenth.
To find the height of the tower from the ground to the vertex of the cone, we can add the height of the cylinder to the slant height of the cone.
We are given that the cylinder is 6 ft. tall and the slant height of the cone is 4 ft.
The height of the tower from the ground to the vertex of the cone is 6 + 4 = <<6+4=10>>10 ft. Answer: \boxed{10}.