Canopy

Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m²?

Correct result:

m₂ =  2.25 kg

Solution:

$$\begin{gathered} v=127\text{ cm}\to \text{ m}=127\mathrm{/}100\text{ m}=1.27\text{ m } \\ r=130\text{ cm}\to \text{ m}=130\mathrm{/}100\text{ m}=1.3\text{ m } \\ h=3.3{\text{kg/m}}^2 \\ {s}^2=v^2+r^2 \\ s=\sqrt{v^2+r^2}=\sqrt{1.27^2+1.3^2}\doteq 1.8174\text{ m } \\ S=\pi \cdot r\cdot s=3.1416\cdot 1.3\cdot 1.8174\doteq 7.4223{\text{m}}^2 \\ {m}_2=S\mathrm{/}h=7.4223\mathrm{/}3.3=2.25\text{ kg} \end{gathered}$$

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