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:

$$ u = π * d $$

  • 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:

  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:

$$ V = 1/3 * π * r ^ 2 * h $$

$$ 3 * V / π = r ^ 2 * h $$

$$ (3 * V) / (π * h) = r ^ 2 $$

$$ sqrt ((3 * V) / (π * h)) = r $$