Question

a satellite launch rocket has a cylindrical fuel tank. the fuel tank can cubic meters of fuel. if the tank measures d meters across, what is the height of the tank in meters?
a.

b.

c.

d.

e.

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Substitute \(r=\frac{d}{2}\) into the volume formula

We get \(V=\pi(\frac{d}{2})^{2}h=\frac{\pi d^{2}h}{4}\). Then, solve for \(h\). Multiply both sides of the equation by \(4\) to get \(4V=\pi d^{2}h\).

Step3: Isolate \(h\)

Divide both sides of the equation \(4V = \pi d^{2}h\) by \(\pi d^{2}\). So, \(h=\frac{4V}{\pi d^{2}}\)

Answer:

D. \(\frac{4V}{\pi d^{2}}\)