Flower box

A wooden flower box in the shape of a cuboid has the following external dimensions: length 120 cm, width 15 cm, and height 20 cm. It is made of wooden slats 1.5 cm thick.

a) At least how many m² of slats were needed to make it? Calculate according to the external dimensions.

b) How many liters of soil will fit in the box if we fill it to the brim?

Correct answer:

S =  0.72 m²
V =  28.08 l

Step-by-step explanation:

$$\begin{gathered} a=120\text{cm}\to \text{m}=120:100\text{m}=1.2\text{m} \\ b=15\text{cm}\to \text{m}=15:100\text{m}=0.15\text{m} \\ c=20\text{cm}\to \text{m}=20:100\text{m}=0.2\text{m} \\ S=a\cdot b+2\cdot (a+b)\cdot c=1.2\cdot 0.15+2\cdot (1.2+0.15)\cdot 0.2=0.72{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} h=1.5\text{cm}\to \text{m}=1.5:100\text{m}=0.015\text{m} \\ {V}_1=(a-2\cdot h)\cdot (b-2\cdot h)\cdot c=(1.2-2\cdot 0.015)\cdot (0.15-2\cdot 0.015)\cdot 0.2\doteq 0.0281{\text{m}}^3 \\ V=V_1\to \text{l}=V_1\cdot 1000\text{l}=0.0281\cdot 1000\text{l}=28.08\text{l}=28.08\text{l} \end{gathered}$$

Try another example