# Dipstick problem (volume of a cylinder)

• dipique
In summary, you need to find the angle between the x-axis and the line connecting the center of the circle with the points where the x-axis intersects the circle. This angle is the area beneath the x-axis.
dipique
There is a problem I'm doing that I understand except for one part. There is a cylinder lying flat, and I want to measure the percentage of fluid in the cylinder by lowering a dipstick inside. In order to do this, I need to find out the height of the fluid when the cylinder is 10% full, 20% full, etc. Here is the question for the part of the problem I can't do:

There is a circle with a radius of 5 bisected by the y-axis. If we move it up and down the y-axis, different percentages of the circle will be above and below the x-axis. What I need to find out is how to relate the percentage below/above the x-axis (either would work) to the distance between the bottom of the circle and the x-axis.

So: we'll start with the circle sitting right on top of the x-axis. 100% of the circle area is above the x-axis. If we want to move it down so that 10% of the circle's area is below the x-axis, how many units would the circle have to be moved down?

Dan

I just got an idea, but I don't think I know enough to make it work. One solution (I think) is to create a triangle connecting the center of the circle with the two points where the x-axis intersects the circle. That angle forms both a wedge of the circle and a triangle; subtract the triangle from the wedge, and there is the area beneath the x-axis. Since we knew the radius of the circle, finding the percentage would be simple. Unfortunately, I'm not good enough with trig to push this through. Help?

All right, I got the answer. If anybody finds this and can't figure it out, feel free to shoot me an e-mail.

Dan

## What is the dipstick problem?

The dipstick problem is a classic mathematical problem that involves finding the volume of a cylinder using only a dipstick (a long, thin measuring tool used to check the level of liquid in a container).

## How do you solve the dipstick problem?

To solve the dipstick problem, you need to measure the height and diameter of the cylinder with the dipstick. Then, you can use the formula V = πr^2h (where V is the volume, r is the radius, and h is the height) to calculate the volume of the cylinder.

## What is the formula for calculating the volume of a cylinder?

The formula for calculating the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.

## Can the dipstick problem be applied to any type of cylinder?

Yes, the dipstick problem can be applied to any type of cylinder, as long as you have the necessary measurements (height and diameter) and use the correct formula.

## Are there any practical applications for the dipstick problem?

Yes, the dipstick problem has practical applications in fields such as engineering, architecture, and manufacturing, where the volume of cylinders needs to be calculated for various purposes.

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