What is a cube made of?

How much packaging do you need?

Do you also like to receive parcels? Or do you order a lot from online mail order companies?

You can already calculate how much fits in there: that is the volume of a cuboid.


Image: Deutsche Post DHL Group

And how much cardboard does it take to make a package? That is the surface of the cuboid.

A cube is a special parallelepiped.

Calculate the surface of a cube

A cube with the edge length a $$ = $$ 4 cm is given.

If you unfold the cube to form a net, you will see that it has 6 square faces of the same size.

First you calculate a square area:

$$ A = a * a $$

$$ A = 4 $$ $$ cm * 4 $$ $$ cm $$

$$ A = 16 $$ $$ cm ^ 2 $$

Since there are 6 times this area, you do the math for the surface of the cube:

$$ O = 6 * A $$

$$ O = 6 * 16 $$ $$ cm ^ 2 $$

$$ O = 96 $$ $$ cm ^ 2 $$

This is how it works faster:

You can also summarize everything in one formula:

$$ O = 6 * a * a $$

$$ O = 6 * 4 $$ $$ cm * 4 $$ $$ cm $$

$$ O = 96 $$ $$ cm ^ 2 $$

The following applies to the surface of the cube: $$ O = 6 * a * a = 6 * a ^ 2 $$

Area of ​​a square:
$$ A = a * a = a ^ 2 $$!

The surface area is given in cm² (read: square centimeters). $$ cm $$ $$ * $$ $$ cm $$ $$ = $$ $$ cm ^ 2 $$

Calculate the surface of a cuboid

A cuboid with the edge lengths a $$ = $$ 5 cm is given,
b $$ = $$ 3 cm, c $$ = $$ 2 cm.

If you unfold the cuboid to form a network, you will see that it has 3 different rectangles, each of which appears twice.



You calculate the individual areas:

$$ A_1 = a * b $$
$$ = 5 $$ $$ cm * 3 $$ $$ cm $$
$$ = 15 $$ $$ cm ^ 2 $$

$$ A_2 = a * c $$
$$ = 5 $$ $$ cm * 2 $$ $$ cm $$
$$ = 10 $$ $$ cm ^ 2 $$

$$ A_3 = b * c $$
$$ = 3 $$ $$ cm * 2 $$ $$ cm $$
$$ = 6 $$ $$ cm ^ 2 $$

Since there are all 3 surfaces twice, the following applies to the calculation of the surface of a cuboid:

$$ O = 2 * A_1 + 2 * A_2 + 2 * A_3 $$

$$ O = 2 * 15 $$ $$ cm ^ 2 + 2 * 10 $$ $$ cm ^ 2 + 2 * 6 $$ $$ cm ^ 2 $$

$$ O = 30 $$ $$ cm ^ 2 + 20 $$ $$ cm ^ 2 + 12 $$ $$ cm ^ 2 $$

$$ O = 62 $$ $$ cm ^ 2 $$

This is how it works faster:

You can also summarize everything in one formula.

$$ O = 2 * a * b + 2 * a * c + 2 * b * c $$

$$ O = 2 * 5 $$ $$ cm * 3 $$ $$ cm + 2 * 5 $$ $$ cm * 2 $$ $$ cm + 2 * 3 $$ $$ cm * 2 $$ $$ cm $$

$$ O = 30 $$ $$ cm ^ 2 + 20 $$ $$ cm ^ 2 + 12 $$ $$ cm ^ 2 $$

$$ O = 62 $$ $$ cm ^ 2 $$

The following applies to the surface of the cuboid: $$ O = 2 * a * b + 2 * a * c + 2 * b * c $$.
It is allowed not to write down the painting points:
$$ O = 2ab + 2ac + 2bc $$

Area of ​​a rectangle:
$$ A = a * b $$
$$ cm $$ $$ * $$ $$ cm $$ $$ = $$ $$ cm ^ 2 $$


Point before line calculation!