# 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!