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 boards 1.5 cm thick.

a) What is the minimum area of boards needed to make it? Calculate based on the external dimensions.

b) How many litres of soil will fit in the box if filled to the brim?

Final Answer:

S =  0.72 m²
V =  28.08 l

Step-by-step explanation:

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

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

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