Metal sheets

How much metal sheet is needed to produce 8 gutters 4 m long and 12 cm in diameter? During production, joints calculate at 3% of total consumption.

Correct answer:

A =  6.2128 m²

Step-by-step explanation:

$$\begin{gathered} D=12\text{ cm}\to \text{ m}=12\mathrm{/}100\text{ m}=0.12\text{ m } \\ r=D\mathrm{/}2=0.12\mathrm{/}2={\displaystyle \frac{3}{50}}=0.06\text{ m } \\ l=8\cdot 4=32\text{ m } \\ {S}_1=\pi \cdot D\cdot l=3.1416\cdot 0.12\cdot 32\doteq 12.0637{\text{m}}^2 \\ q=3\mathrm{\%}=1+{\displaystyle \frac{3}{100}}=1.03 \\ A=S_1\mathrm{/}2\cdot q=12.0637\mathrm{/}2\cdot 1.03=6.2128{\text{m}}^2 \end{gathered}$$

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