Boxes

Cuboid-shaped boxes without a lid are to be painted on all sides, both inside and outside. The base dimensions are 60 cm × 30 cm and the height is 12 cm. How many cans of paint are needed to paint 10 such boxes if one can covers 4 m²?

Final Answer:

n =  2

Step-by-step explanation:

$$\begin{gathered} a=60\text{cm} \\ b=30\text{cm} \\ c=12\text{cm} \\ {S}_1=a\cdot b+2\cdot (a+b)\cdot c=60\cdot 30+2\cdot (60+30)\cdot 12=3960{\text{cm}}^2 \\ {S}_2=2\cdot S_1=2\cdot 3960=7920{\text{cm}}^2 \\ {S}_{10}=10\cdot S_2=10\cdot 7920=79200{\text{cm}}^2 \\ {S}_0=4{\text{m}}^2\to {\text{cm}}^2=4\cdot 10000{\text{cm}}^2=40000{\text{cm}}^2 \\ {n}_0=S_{10}/S_0=79200/40000=\frac{99}{50}=1\frac{49}{50}=1.98 \\ n=\lceil n_0\rceil =\lceil 1.98\rceil =2 \end{gathered}$$

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