Question

A spherical tank is 4 m tall and therefore has a capacity of about 33500 l (note that 4m is its diameter, and one cubic meter is 1000 l). You have been asked to put level lines on the tank showing the depths where the tank contains 10000, 20000, and 30000 l of liquid.

Answer 1

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.

Volume of the spherical tank

The volume of the spherical tank is calculated by using the following formula as shown below;

$V = \frac{4}{3} \pi r^3= \frac{4}{3} \pi (\frac{d}{2} )^3= \frac{4}{3} \pi \frac{d^3}{8} = \frac{1}{6} \pi d^3$

The depth of the tank at different capacity level

The level lines on the tank showing the depths of different capacities is calculated as follows;

$(\frac{1}{6} \pi d^3 )k = V\\\\k = \frac{V}{d^3} \\\\\frac{V_1}{d_1^3} = \frac{V_2}{d_2^3}\\\\d_2 = \sqrt[3]{\frac{V_2d_1^3}{V_1} }\\\\for \ 10,000 \ L\\\\d_2 = \sqrt[3]{\frac{10,000\times 4^3}{33,500} }\\\\d_2 = 2.65 \ m\\\\for \ 20,000 L\\\\d_3 = \sqrt[3]{\frac{20,000\times 4^3}{33,500} }\\\\d_3 = 3.36\ m\\\\d_4 = \sqrt[3]{\frac{30,000\times 4^3}{33,500} }\\\\d_4 = 3.85 \ m$

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.

Learn more about volume of spherical tank here: brainly.com/question/24480057

Answer 2

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

Volume of a spherical tank

The volume of a spherical tank can be calculated as

V = $\frac{4}{3}\pi r^3 = \frac{1}{6}\pi d^3$

Next step : calculate the level lines at various capacities

applying equation above

V = $(\frac{1}{6} \pi d^3)k$

where k = v / d³

therefore : di = $\sqrt[3]{\frac{Vid^3}{V_{1} } }$  ------- ( 1 )

where : di = level line , Vi = volume of tank , V1 = capacity of tank = 33500

             d = diameter of tank

Applying equation ( 1 )

• For Vi = 10000 l

   level line ( di ) = 2.65 m

• For Vi = 20000 l

 level line ( di ) = 3.36 m

• For Vi = 30000 l

  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

Learn more about spherical tank volume : brainly.com/question/11279298