Question

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?
a. \\(\frac{4v}{\pi d^{2}}\\)
b. \\(\frac{4v}{\pi d}\\)
c. \\(\frac{v}{\pi d^{2}}\\)
d. \\(\frac{v}{\pi d}\\)
e. \\(\frac{vd}{\pi}\\)

Explanation:

Step1: Recall cylinder - volume formula

The volume formula for a cylinder is $V=\pi r^{2}h$, where $V$ is the volume, $r$ is the radius and $h$ is the height. Given that the diameter $d = a$ meters, then the radius $r=\frac{a}{2}$ meters.

Step2: Solve for height $h$

We have $V=\pi(\frac{a}{2})^{2}h$. Rearranging the formula for $h$, we get $h=\frac{V}{\pi(\frac{a}{2})^{2}}=\frac{4V}{\pi a^{2}}$.

Answer:

B. $\frac{4V}{\pi a^{2}}$