Consumption 15663

The cone-shaped sheet metal roof has a base diameter of 80 cm and a height of 60 cm. Calculate the paint consumption for painting this roof if 1 kg of paint is consumed per 6 m² of sheet metal.

Correct answer:

m =  0.13 kg

Step-by-step explanation:

$$\begin{gathered} v=80\text{cm}\to \text{m}=80:100\text{m}=0.8\text{m} \\ D=60\text{cm}\to \text{m}=60:100\text{m}=0.6\text{m} \\ c=6{\text{m}}^2\text{/kg} \\ r=D/2=0.6/2=\frac{3}{10}=0.3\text{m} \\ {s}^2=v^2+r^2 \\ s=\sqrt{v^2+r^2}=\sqrt{0.8^2+0.3^2}\doteq 0.8544\text{m} \\ S=\pi \cdot r\cdot s=3.1416\cdot 0.3\cdot 0.8544\doteq 0.8053{\text{m}}^2 \\ m=S/c=0.8053/6=0.13\text{kg} \end{gathered}$$

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