How to Find the Height of a Cylindrical Fuel Tank
Question:
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 / πd²
b) 4V / d²
c) V / πd²
d) 4V / πd²
e) 8V / πd²
Answer:
The height (h) of a cylindrical tank is determined by rearranging the formula for the volume of the cylinder, thus h = 4V / πd² (option d).
To find the height of the cylindrical fuel tank, we can use 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. In this case, the diameter (d) of the tank is given, so the radius (r) is d/2.
Substitute the radius into the volume formula: V = π (d/2)² h. Simplifying this equation, we get V = π (d²/4) h. To solve for the height h, we rearrange the equation to get h = V / πr² = V / π(d/2)² = V / π(d²/4) = 4V / πd².
Therefore, the height of the cylindrical fuel tank is 4V / πd². This calculation allows us to determine the necessary height for the tank based on its diameter and volume capacity.