To answer this question, we need to have into account the formula for the volume of a cylinder. This formula is given by:
[tex]V=\pi\cdot r^2\cdot h[/tex]
1. We have that pi is approximately equal to 3.1415926535...
2. The radius is half of the diameter. In this case, the diameter is 6 feet. Therefore, the radius is 3 feet.
3. The height of the storage tank (cylinder) is h = 10 feet.
Hence, we can plug all of these values into the formula, and we can get the value for the total volume of this cylinder:
[tex]V=\pi\cdot(3^{}ft)^2\cdot10ft\Rightarrow V=\pi\cdot9\cdot10\Rightarrow V=90\pi ft^3[/tex]
Now, since the tank is half-filled with oil, we have that the oil, in cubic feet, in the cylindrical tank is half of the value of the previous value, that is:
[tex]\frac{1}{2}V=\frac{1}{2}\cdot(90\pi ft^3)=45\pi ft^3[/tex]
Hence, the current volume of oil in the cylindrical tank is:
[tex]45\pi ft^3[/tex]
(Option C).
