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.(1 point)
Responses
19.0 ft.
19.0 ft.
18.5 ft.
18.5 ft.
8.6 ft.
8.6 ft.
16.6 ft.
To solve this problem, we can use the Pythagorean theorem to find the height of the cone.
First, let's find the radius of the cylinder. Since the diameter is given as 6 ft, the radius is half of that, which is 6/2 = 3 ft.
Next, let's find the height of the cone. The slant height of the cone is given as 4 ft, and the radius is 3 ft. We can use the Pythagorean theorem to find the height.
Let's denote the height of the cone as h.
Using the Pythagorean theorem, we have:
h^2 = (4^2) - (3^2)
h^2 = 16 - 9
h^2 = 7
h = √7
Now, let's find the total height of the tower by adding the height of the cylinder (6 ft) and the height of the cone (√7 ft).
Total height = 6 + √7
To the nearest tenth, the height of the tower from the ground to the vertex of the cone is 6 + √7 ≈ 8.6 ft.
Therefore, the correct answer is 8.6 ft.