To find the height of the cylindrical fuel tank, we need to start with the volume formula of a cylinder and solve for the height.
The formula for 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 cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder,
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
We are given the diameter [tex]\( d \)[/tex] of the cylinder, which is twice the radius. Therefore, we can express the radius [tex]\( r \)[/tex] in terms of the diameter [tex]\( d \)[/tex]:
[tex]\[ r = \frac{d}{2} \][/tex]
We substitute [tex]\( r \)[/tex] into the volume formula:
[tex]\[ V = \pi \left(\frac{d}{2}\right)^2 h \][/tex]
Next, we simplify the expression inside the parentheses:
[tex]\[ V = \pi \left(\frac{d^2}{4}\right) h \][/tex]
This simplifies further to:
[tex]\[ V = \frac{\pi d^2}{4} h \][/tex]
Now, to solve for the height [tex]\( h \)[/tex], we rearrange the formula to isolate [tex]\( h \)[/tex] on one side:
[tex]\[ h = \frac{4V}{\pi d^2} \][/tex]
Thus, the height of the cylindrical fuel tank in meters is:
[tex]\[ \boxed{\frac{4 V}{\pi d^2}} \][/tex]
So the correct answer is:
A. [tex]\(\frac{2 V}{\pi d^2}\)[/tex]
is incorrect.
B. [tex]\(\frac{4 V}{d}\)[/tex]
is incorrect.
C. [tex]\(\frac{V}{\pi^2}\)[/tex]
is incorrect.
D. [tex]\(\frac{4 V}{\pi d^d}\)[/tex]
is incorrect.
E. [tex]\(\frac{8 V}{\pi c^2}\)[/tex]
is incorrect.
The height of the fuel tank in meters is:
[tex]\[ \boxed{\frac{4 V}{\pi d^2}} \][/tex]
