# Volume of a Cylindrical Satellite Fuel Tank Calculation

## How to calculate the height of a cylindrical fuel tank based on its volume and diameter?

A satellite launch rocket has a cylindrical fuel tank that can hold V cubic meters of fuel. If the tank measures D meters across, what is the height of the tank in meters?

a. 2V / (πD^2) b. 4V / D^2 c. V / (πD^2) d. 4V / (πD^2) e. 8V / (πD^2)

## Answer:

The height of the cylindrical satellite fuel tank can be determined using the formula for the volume of a cylinder by substituting the radius with diameter/2 and rearranging the formula to solve for height, the correct formula will be 4V / (πD²).

Explanation:

This question refers to the mathematics of a cylindrical fuel tank's geometry, specifically concerning its height when other dimensions and volume are known.

We can solve this using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.

The diameter D is twice the radius, hence, radius r = D/2. Substitute r with D/2 in the volume formula, so we get V = π(D/2)²h = πD²/4 * h.

To find the height h, you need to rearrange the formula to solve for h, giving us h = 4V / (πD²).

Therefore, the answer is (d) 4V / (πD²).