|
Question 1181778: A factory's pressure tank rests on the upper base of a vertical pipe whose inside diameter is 1 and 1/2 ft. and whose length is 40 ft. The tank is a vertical cylinder surmounted by a cone, and it has a hemispherical base. If the alti tudes of the cylinder and the cone are respectively 6 ft. and 3 ft. and if all three parts of the tank have an inside diameter of 6 ft., find the volume of water in the tank and pipe when full.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the total volume of water in the tank and pipe:
**1. Calculate the volume of the pipe:**
* The pipe is a cylinder.
* Pipe diameter = 1.5 ft, so the radius is 1.5 ft / 2 = 0.75 ft.
* Pipe length (height) = 40 ft.
* Volume of a cylinder = π * radius² * height
* Pipe volume = π * (0.75 ft)² * 40 ft ≈ 70.69 ft³
**2. Calculate the volume of the cylindrical part of the tank:**
* Tank diameter = 6 ft, so the radius is 6 ft / 2 = 3 ft.
* Cylinder height = 6 ft.
* Cylinder volume = π * (3 ft)² * 6 ft ≈ 169.65 ft³
**3. Calculate the volume of the conical part of the tank:**
* Cone radius = 3 ft (same as the cylinder).
* Cone height = 3 ft.
* Volume of a cone = (1/3) * π * radius² * height
* Cone volume = (1/3) * π * (3 ft)² * 3 ft ≈ 28.27 ft³
**4. Calculate the volume of the hemispherical base:**
* Hemisphere radius = 3 ft (same as the cylinder and cone).
* Volume of a hemisphere = (2/3) * π * radius³
* Hemisphere volume = (2/3) * π * (3 ft)³ ≈ 56.55 ft³
**5. Calculate the total volume:**
* Total volume = Pipe volume + Cylinder volume + Cone volume + Hemisphere volume
* Total volume ≈ 70.69 ft³ + 169.65 ft³ + 28.27 ft³ + 56.55 ft³ ≈ 325.16 ft³
**Therefore, the volume of water in the tank and pipe when full is approximately 325.16 cubic feet.**
|
|
|
| |
