Question #205508

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.

Expert's answer

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):

Tank volume:

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:

So

**Answer**: "103.5\\pi \\approx 325.155 ft^3"

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