# 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 bodyLike 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 \$\$

• 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 \$\$

kapiert.decan do more:

• interactive exercises
and tests
• individual classwork trainer
• Learning manager

### 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:

1. 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 \$\$

2. 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 \$\$