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# Answer to Question #205508 in Civil and Environmental Engineering for Mika

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.

1
2021-06-11T06:11:05-0400

The volume of the water:

"V=V_P+V_T"

where the volume of the pipe (the volume of a cylinder 40 ft high and 1.5 ft in diameter):

"V_P =\\pi H_p \\frac {D^2_p}{4}=\\pi \\cdot 40ft \\cdot \\frac {2.25} 4 ft^2 =22.5\\pi \\space ft^3"

Tank volume:

"V_T =V_{hs}+V_{cyl}+V_{con}"

volume of a hemisphere with a diameter of 6 ft:

"V_{hs}=\\frac 1 2 \\frac 4 3 \\pi \\frac {D^3_{hs} }{8}=\\frac 1 {12} \\pi \\cdot216 ft^3=18 \\pi \\space ft^3"

volume of a cylinder 6 ft high and 6 ft in diameter:

"V_{cyl} =\\pi H_{cyl} \\frac {D^2_{cyl}}{4}=\\pi \\cdot 6ft \\cdot \\frac {36} 4 ft^2 =54\\pi \\space ft^3"

volume of a cone 3 ft high and 6 ft in diameter:

"V_{con}=\\frac{H_{con}}{3} \\pi \\frac {D^2_{con}}{4}=\\pi \\frac{3ft \\cdot 36 ft^2}{12}=9 \\pi \\space ft^3"

So

"V=22.5\\pi+18\\pi+54\\pi+9\\pi=103.5\\pi \\approx 325.155 ft^3"

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