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. 

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):

"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"


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

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

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be the first!

Leave a comment

New on Blog