A factory's pressure tank rests on the upper base of a vertical pipe whose inside diameter is 1 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 altitudes 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 the water in the tank and pipe when full.
The volume of the water:
where the volume of the pipe (the volume of a cylinder 40 ft high and 1.5 ft in diameter):
volume of a hemisphere with a diameter of 6 ft:
volume of a cylinder 6 ft high and 6 ft in diameter:
volume of a cone 3 ft high and 6 ft in diameter: