Painting a column

How many kg of paint do we need to paint a column in the shape of a regular triangular prism with a base edge of 2.5 m long and a height to the base edge of 2 m, if 1 kg of paint is enough for 25 m² of paint? The column is 10 m high.

Correct answer:

m =  3.2 kg

Step-by-step explanation:

$$\begin{gathered} a=2.5\text{m} \\ {h}_1=2\text{m} \\ {h}_2=10\text{m} \\ {S}_1=\frac{a\cdot h_1}{2}=\frac{2.5\cdot 2}{2}=\frac{5}{2}=2.5{\text{m}}^2 \\ {S}_2=3\cdot a\cdot h_2=3\cdot 2.5\cdot 10=75{\text{m}}^2 \\ S=2\cdot S_1+S_2=2\cdot 2.5+75=80{\text{m}}^2 \\ {S}_0=25{\text{m}}^2\text{/kg} \\ m=S/S_0=80/25=3.2\text{kg} \end{gathered}$$

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