To determine the height of a cylindrical fuel tank that has a volume [tex]\( V \)[/tex] cubic meters and a diameter [tex]\( d \)[/tex] meters, we can use the formula for the volume of a cylinder. The volume [tex]\( V \)[/tex] of a cylinder is given by:
[tex]\[ V = \pi r^2 h \][/tex]
Where:
- [tex]\( r \)[/tex] is the radius of the cylindrical tank
- [tex]\( h \)[/tex] is the height of the cylindrical tank
Since the diameter [tex]\( d \)[/tex] of the cylinder is given, the radius [tex]\( r \)[/tex] can be obtained by:
[tex]\[ r = \frac{d}{2} \][/tex]
Substituting the radius into the volume formula, we get:
[tex]\[ V = \pi \left( \frac{d}{2} \right)^2 h \][/tex]
Simplifying the equation, we get:
[tex]\[ V = \pi \frac{d^2}{4} h \][/tex]
To solve for the height [tex]\( h \)[/tex], we rearrange the equation:
[tex]\[ h = \frac{4V}{\pi d^2} \][/tex]
Thus, the height of the tank is:
[tex]\[ h = \frac{4V}{\pi d^2} \][/tex]
We need to match this result with the given options:
A. [tex]\(\frac{2 V}{x d^2}\)[/tex]
B. [tex]\(\frac{4 V}{d^2}\)[/tex]
C. [tex]\(\frac{V}{\pi c^2}\)[/tex]
D. [tex]\(\frac{4 V}{\pi d^2}\)[/tex]
E. [tex]\(\frac{8 V}{\pi d^2}\)[/tex]
The correct option that matches our derived formula is:
D. [tex]\(\frac{4 V}{\pi d^2}\)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{D. \frac{4 V}{\pi d^2}} \][/tex]
