# 55037c 1000 ml corresponds to the number of cups

## Calculate the volume of a cup - this is how it works

Have you always wondered how big the volume of your favorite cup actually is and how you can determine it as easily as possible? No problem, all you need is a measuring cup, some water, or a few simple math formulas.

### What you need:

- measuring cup
- water
- Volume formula
- Tape measure

### Determine the volume of a cup very easily

By the volume of a cup you will probably understand how much content (e.g. water) your cup actually fits. You can very easily determine the approximate capacity of a cup if you use a measuring cup, some water and the cup itself.

- Now fill your cup at the tap up to the top with water. Now pour the water into a measuring cup, being careful not to spill any water during this process.
- You can now easily determine the capacity (or volume) of the cup by reading the value on the measuring cup. 1dm applies
^{3}= 1l. For example, if you read the value 280 ml, this corresponds to a content of 0.28dm^{3}(Rule of three).

### Calculate the volume of the cup using formulas

- You can also approximate the volume of a cup using mathematical formulas. It depends on the shape of your cup.
- Many common cups are in the shape of a cylinder. For the volume of a cylinder, V = base area * height, where the base area is derived from G = πr
^{2}can be calculated. The easiest way to measure the height of the cup is with a tape measure that is as accurate as possible. - To determine the base area, you need the radius. You can easily determine this by measuring the diameter again with the measuring tape and then dividing it by two.
- Now calculate the volume of your cup.
- Often, cups also get wider towards the top. These then have approximately the shape of a truncated cone. To calculate such a cup volume, you need to measure the diameter of the two base circles and determine the height. It can be helpful to make a sketch on a piece of paper.
- If you have the sketch in front of you, you can determine the apex of the cone by extending the side lines.
- You can now determine the volume of the truncated cone by subtracting the volume of the small cone from the volume of the large cone. Alternatively, you can work directly with the formulas for the truncated cone (from the formula collection).

It gets tricky with even more difficult forms. As long as these are symmetrical, you can approximate a side line by a function (make a sketch!), Get the shape of the cup by rotating it around the x-axis and then determine its volume by integration.

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