\( \rightarrow \) Unit Posttest 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, what is the height of the tank in meters? \[ \begin{array}{ll}\text { A. } \frac{2 V}{\pi d^{2}} \\ \text { B. } \frac{4 V}{d^{2}} \\ \text { C. } \frac{V}{\pi d^{2}} \\ \text { D. } \frac{4 V}{\pi d^{2}} \\ \text { E. } \frac{8 V}{\pi d^{2}}\end{array} \]

To determine the height \( h \) of the cylindrical fuel tank, we can use the formula for the volume of a cylinder: \[ V = \pi r^2 h \] where: - \( V \) is the volume, - \( r \) is the radius, - \( h \) is the height. Given that the tank measures \( d \) meters across (which is the diameter), the radius \( r \) is: \[ r = \frac{d}{2} \] Substitute \( r = \frac{d}{2} \) into the volume formula: \[ V = \pi \left(\frac{d}{2}\right)^2 h = \pi \frac{d^2}{4} h \] Solving for \( h \): \[ h = \frac{V}{\pi \frac{d^2}{4}} = \frac{4V}{\pi d^2} \] Therefore, the height of the tank is: \[ h = \frac{4V}{\pi d^2} \] **Answer:** **D.** \(\frac{4 V}{\pi d^{2}}\)