a satellite launch rocket has a cylindrical fuel tank. the fuel tank can hold v cubic meters of fuel. if the…

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?\na. $\frac{2v}{pi d^{2}}$\nb. $\frac{4v}{d^{2}}$\nc. $\frac{v}{pi d^{2}}$\nd. $\frac{4v}{pi d^{2}}$\ne. $\frac{8v}{pi d^{2}}$

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?\na. $\frac{2v}{pi d^{2}}$\nb. $\frac{4v}{d^{2}}$\nc. $\frac{v}{pi d^{2}}$\nd. $\frac{4v}{pi d^{2}}$\ne. $\frac{8v}{pi d^{2}}$

Answer

Answer:

E. $\frac{4V}{\pi d^{2}}$

Explanation:

Step1: Recall volume formula for cylinder

The volume formula for a cylinder is $V = \pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height.

Step2: Find radius from diameter

Given diameter $d$, radius $r=\frac{d}{2}$.

Step3: Substitute radius into volume formula

$V=\pi(\frac{d}{2})^{2}h=\frac{\pi d^{2}}{4}h$.

Step4: Solve for height $h$

We can rewrite the equation $V = \frac{\pi d^{2}}{4}h$ to solve for $h$. Multiply both sides by $\frac{4}{\pi d^{2}}$, we get $h=\frac{4V}{\pi d^{2}}$.