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a water tank is used to store water for livestock is in the shape of a cylinder with a diameter of 5 feet and a hight of 6 feet. the tank has sprung a leak. it is leaking water at a rate of 0.75 cubic feet per hour. if the tank is full how long should it take for the tank to empty

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ANSWER


157.08\text{ hours}

Step-by-step explanation

First, we have to find the volume of the cylindrical tank.

The volume of a cylinder is given as:


V=\pi\cdot r^2\cdot h

where r = radius; h = height

We are given the diameter of the tank (5 feet). Radius is half of the diameter, so:


\begin{gathered} r=(D)/(2) \\ r=(5)/(2) \\ r=2.5ft \end{gathered}

Therefore, the volume of the tank is:


\begin{gathered} V=\pi\cdot2.5^2\cdot6 \\ V=117.81ft^3 \end{gathered}

The tank is leaking water at a rate of 0.75 ft³ per hour.

To find the time it will take for the tank to be empty, we have to divide the volume of the tank by the rate at which it is leaking.

That is:


\begin{gathered} \text{Time}=(117.81)/(0.75) \\ \text{Time}=157.08\text{ hours} \end{gathered}

That is the time it will take for the tank to be empty.

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