Answer: [tex]h=\frac{4V}{\pi d^2}[/tex] meters
Step-by-step explanation:
Given: A satellite launch rocket has a cylindrical fuel tank. The fuel tank can hold V cubic meters of fuel. If the tank measures d meters across.
Then radius of the cylinder =[tex]\frac{d}{2}[/tex]
Let h be the height of the cylindrical fuel tank.
We know that the volume of cylinder is given by :-
[tex]\text{Volume}=\pi r^2h[/tex]
Now, for the volume of cylindrical tank we have :-
[tex]V=\pi (\frac{d}{2})^2h\\\\\Rightarrow V=\pi(\frac{d^2}{4})h\\\\\Rightarrow\ h=\frac{4V}{\pi d^2}[/tex]
Hence, the height of the tank = [tex]h=\frac{4V}{\pi d^2}[/tex] meters
