The conical roof

The conical roof above the warehouse has a diameter of the lower part (base) d = 11.2 m and a height v = 3.3 m. How many rectangular steel plates with dimensions of 1.4 m and 0.9 m were needed to produce this roof if the seams and waste required an increase in their consumption by 10 percent?

Correct answer:

n =  100

Step-by-step explanation:

$$\begin{gathered} d=11.2\text{m} \\ v=3.3\text{m} \\ a=1.4\text{m} \\ b=0.9\text{m} \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ r=d/2=11.2/2=\frac{28}{5}=5\frac{3}{5}=5.6\text{m} \\ s=\sqrt{v^2+r^2}=\sqrt{3.3^2+5.6^2}=\frac{13}{2}=6\frac{1}{2}=6.5\text{m} \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 5.6\cdot 6.5\doteq 114.354{\text{m}}^2 \\ {S}_2=S_1\cdot q=114.354\cdot 1.1\doteq 125.7894{\text{m}}^2 \\ {S}_3=a\cdot b=1.4\cdot 0.9=\frac{63}{50}=1\frac{13}{50}=1.26{\text{m}}^2 \\ n=\lceil S_2/S_3\rceil =\lceil 125.7894/1.26\rceil =100 \end{gathered}$$

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