Metal sheets

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

Correct answer:

A =  6.2128 m²

Step-by-step explanation:

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

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