# How to calculate a cone

### What is a cone?

You know cones from construction sites on the street.

Image: Druwe & Polastri

Ice cream cones or tower roofs are also conical.

Images: fotolia.com (unpict), iStockphoto.com (esemelwe)

### And now mathematically

A cone is a geometric body with:

- one
**Circle as a base**, - one
**domed coat** - and one
**top**.

The **Body height h** is the distance between the tip and the base. The connecting line from the edge of the circle to the tip is called **Surface line s**.

### What is the volume of a cone?

Since the cone is a body, it can be filled.

You fill a cone with water and measure it in a measuring cup. This is how you get that **Volume of the cone**. The volume tells you how much liquid fits into a cone.

Great for everyone **body**Like the pyramid, you also calculate the volume **Base area times body height divided by 3**.

How to calculate the volume of a cone:

$$ V = 1/3 * G * h $$

$$ V = 1/3 * π * $$ $$ r ^ 2 * h $$

**Circular formulas:**

$$ G = π * r ^ 2 $$

$$ u = 2 * π * r $$ or:

$$ u = π * d $$

**r**radius**d**diameter**π**Circle number

### This is how you calculate the volume of a cone

A cone is given with $$ r = 3 $$ $$ cm $$ and $$ h = 7 $$ $$ cm $$.

To calculate the volume of the cone, do the following:

Plug the given values into our formula:

$$ V = 1/3 * π * r ^ 2 * h $$

$$ V = 1/3 * π * (3 $$ $$ cm $$$$) ^ 2 * 7 $$ $$ cm $$

$$ V = 65.97 $$ $$ cm ^ 3 $$

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### Calculate the radius for a given volume

A cone with a volume of

$$ V = 84.47 $$ $$ cm ^ 3 $$ and a height of $$ h = 4.2 $$ $$ cm $$.

### To calculate the radius of the cone, do the following:

Plug the given volume and height into the formula:

$$ V = 1/3 * π * r ^ 2 * h $$

$$ 84.47 $$ $$ cm ^ 3 $$ $$ = 1/3 * π * r ^ 2 $$ $$ * $$ $$ 4.2 $$ $$ cm $$Solve the formula for r:

$$ 84.47 $$ $$ cm ^ 3 $$ $$ = 1/3 * π * r ^ 2 $$ $$ * $$ $$ 4.2 cm $$ | $$: 4.2 cm $$ | $$: pi / 3 $$

$$ (3 * 84.47 cm ^ 3) / (pi * 4.2 cm) $$ $$ = r ^ 2 $$ | $$ sqrt () $$

$$ sqrt ((253.41 cm ^ 3) / (pi * 4.2 cm)) $$$$ = r $$

$$ sqrt (19.21 cm ^ 2) = r $$

$$ 4.38 cm = r $$

You can also change the formula first and then insert the values:

$$ V = 1/3 * π * r ^ 2 * h $$

$$ 3 * V / π = r ^ 2 * h $$

$$ (3 * V) / (π * h) = r ^ 2 $$

$$ sqrt ((3 * V) / (π * h)) = r $$

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