The level line at 10,000 liters is 2.65 m, the level line at 20,000 liters is 3.36 m and the level line at 30,000 liters is 3.85 m.
The volume of the spherical tank is calculated by using the following formula as shown below;
[tex]V = \frac{4}{3} \pi r^3= \frac{4}{3} \pi (\frac{d}{2} )^3= \frac{4}{3} \pi \frac{d^3}{8} = \frac{1}{6} \pi d^3[/tex]
The level lines on the tank showing the depths of different capacities is calculated as follows;
[tex](\frac{1}{6} \pi d^3 )k = V\\\\k = \frac{V}{d^3} \\\\\frac{V_1}{d_1^3} = \frac{V_2}{d_2^3}\\\\d_2 = \sqrt[3]{\frac{V_2d_1^3}{V_1} }\\\\for \ 10,000 \ L\\\\d_2 = \sqrt[3]{\frac{10,000\times 4^3}{33,500} }\\\\d_2 = 2.65 \ m\\\\for \ 20,000 L\\\\d_3 = \sqrt[3]{\frac{20,000\times 4^3}{33,500} }\\\\d_3 = 3.36\ m\\\\d_4 = \sqrt[3]{\frac{30,000\times 4^3}{33,500} }\\\\d_4 = 3.85 \ m[/tex]
Thus, the level line at 10,000 liters is 2.65 m, the level line at 20,000 liters is 3.36 m and the level line at 30,000 liters is 3.85 m.
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The level line for 10000 l is : 2.65 m , The level line for 20000 l is : 3.36 m . and The level line for 30000 l is : 3.85 m
Given data :
Diameter of tank ( d ) = 4 m
1 cm³ = 1000 l
The volume of a spherical tank can be calculated as
V = [tex]\frac{4}{3}\pi r^3 = \frac{1}{6}\pi d^3[/tex]
Next step : calculate the level lines at various capacities
applying equation above
V = [tex](\frac{1}{6} \pi d^3)k[/tex]
where k = v / d³
therefore : di = [tex]\sqrt[3]{\frac{Vid^3}{V_{1} } }[/tex] ------- ( 1 )
where : di = level line , Vi = volume of tank , V1 = capacity of tank = 33500
d = diameter of tank
Applying equation ( 1 )
level line ( di ) = 2.65 m
level line ( di ) = 3.36 m
level line ( di ) = 3.85 m
Hence we can conclude that The level line for 10000 l is : 2.65 m , The level line for 20000 l is : 3.36 m . and The level line for 30000 l is : 3.85 m
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