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# A hemispherical tank full of water is emptied by a pipe at the rate of $\dfrac{{25}}{7}$ litres per second. How much time will it take to empty the tank, if the tank is ${\text{3}}$ meters in diameter?

Last updated date: 17th Jul 2024
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Hint: First, let’s calculate the volume of the tank. From that volume let’s take half of it to calculate the time taken to empty that half of the volume of water.

Given,
The diameter of the hemispherical tank is $D = 3m$
Hence the radius will be $R = \dfrac{3}{2}m$
The total volume of the water in the hemispherical tank
$V{\text{ }} = {\text{ }}\dfrac{2}{3}\pi {R^3} \\ V = \dfrac{2}{3}{\text{x}}\dfrac{{22}}{7}{\text{x(1}}{\text{.5}}{{\text{)}}^3}{m^3} \\ {\text{ then }}V = \dfrac{{148500}}{{21}}litres{\text{ (as }}1{m^3} = 1000{\text{ }}litres{\text{)}} \\$
This above volume is the volume of the hemispherical tank.
Volume of the half-emptied tank ${\text{ = }}\dfrac{V}{2}{\text{ = }}\dfrac{{74250}}{{21}}litres$
Given that time required to empty $\dfrac{{25}}{7}$ litres of water is $1$ second.
Hence the time required to empty $1$ litres of water is $\dfrac{7}{{25}}$ seconds.
Now, Time taken to half empty the tank will be equal to
$\dfrac{{74250}}{{21}}litres{\text{ of water = }}\dfrac{7}{{25}}{\text{x}}\dfrac{{74.25}}{{21}}secs{\text{ }} \\ {\text{ }}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\text{ = 990 }}secs. \\ {\text{ = 16}}{\text{.5 }}\min{\text{ ( since 1 minute = 60 seconds)}} \\$
Hence time taken to half empty the tank is ${\text{16}}{\text{.5}}$ minutes.

Note: In order to solve these surface areas and volume problems, you should have command over formulas related to all types of 3D shapes.