Castle painting cans

The castle has a length of 4 m and a cross-section in the shape of a square whose side is 15 cm long. Eight such castles must be painted. One kilogram can is enough for 6 m² of coating. How many cans of paint should be bought?

Final Answer:

n =  4

Step-by-step explanation:

$$\begin{gathered} l=4\text{m} \\ a=15\text{cm}\to \text{m}=15:100\text{m}=0.15\text{m} \\ {S}_1=6{\text{m}}^2 \\ {S}_2=l\cdot 4\cdot a+2\cdot a^2=4\cdot 4\cdot 0.15+2\cdot 0.15^2=\frac{489}{200}=2\frac{89}{200}=2.445{\text{m}}^2 \\ {S}_8=8\cdot S_2=8\cdot 2.445=\frac{489}{25}=19\frac{14}{25}=19.56{\text{m}}^2 \\ {n}_1=S_8/S_1=19.56/6=\frac{163}{50}=3\frac{13}{50}=3.26 \\ n=\lceil n_1\rceil =\lceil 3.26\rceil =4 \end{gathered}$$

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