Question

an oil tank has to be drained for maintenance. The tank is shaped like a that is ft long with a diameter of 2.2 Suppose is drained at a rate of 2.1 ft ^ 3 per minutethe tank starts completely full , how many minutes will it take to empty the tank? Use the value 3.14 for and round your answer to the nearest minutenot round any intermediate computations

Answer 1

The given information is:

- The tank has the shape of a cylinder

- The dimensions of the cylinder are 5 ft long and diameter 2.2 ft.

- The tank is drained at a rate of 2.1 ft^3 per minute.

The volume of the tank is given by the formula:

`V=\pi *((d)/(2))^2*h`

Where d is the diameter and h is the height.

By replacing the known values we obtain the initial volume:

`\begin{gathered} V=3.14*((2.2ft)/(2))^2*5ft \\ V=3.14*(1.1ft)^2*5ft \\ V=3.14*1.21ft^2*5ft \\ V=18.997ft^3 \end{gathered}`

As the drain rate is 2.1 ft^3 per minute, the time that is needed to empty the tank is:

`\frac{18.997ft^3}{2.1ft^3\text{ / min}}=9.04\text{ min}`

The answer is 9 minutes.