Question #241404

A closed right cylindrical tank with a height of 8 m and 3 m in diameter contains water to a depth of 5m. If the tank is laid in a horizontal position, find the depth of water.

Expert's answer

"cos\\frac{1}{2}\u03b8=0.5\/2.5"

"\u03b8=156.926^\u2218 "

"\u03b1=360^\u2218\u2212\u03b8=360^\u2218\u2212156.926^\u2218"

"\u03b1=203.074^\u2218"

Area of cross section:

"A_b=1\/2r^2(\u03b1_{rad}+sin\u03b8_{deg})\n"

"A_b=12.3 ft^2 "

Volume of water:

"V_w=A_bL=12.3(8)"

"V_w=98.4"

Depth of water in vertical position:

"Vw=\u03c0r^2h"

"98.4=\u03c0(2.5^2)h \n"

"h=5.01\\space ft \\space\\space answer"

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