A cylindrical gas tank with radius 10ft is lying on its side.
When the height of the (liquid) gas is 10ft, the tank is half full.
What will be the height of the gas when the tank is 1/4 full?
*I assigned a constant length of the cylinder in order to plug the values into an online calculator for find the volume of liquid in a horizontal cylinder, divide that by two, and solve for the height variable. The online calculator produced 5.96027 however, the chapter I am studying is volumes by integration & I cannot cite an online calculator. I have no idea how to do this but I am assuming it involves integration (possibly revolved a semicircle with radius 10 about the y-axis) or some other form of calculus.
Hint: The length of the cylinder doesn't matter. All you care about is the area of the circle at the end and what fraction is covered by gas. You need to find the height of a circular segment with area half of the semicircle. You can do this without integration, just using geometry.