Sphere-shaped 20723

The sphere-shaped reservoir has a volume of 282 hl. Calculate the material consumption in m² for its production, assuming 8% for joints and waste, and round the final result to the nearest total.

Correct answer:

S =  49 m²

Step-by-step explanation:

$$\begin{gathered} V=282\text{hl}\to {\text{m}}^3=282:10{\text{m}}^3=28.2{\text{m}}^3 \\ V=\frac{4}{3}\pi r^3 \\ r=\sqrt[3]{3\cdot V/(4\pi )}=\sqrt[3]{3\cdot 28.2/(4\cdot 3.1416)}\doteq 1.8882\text{m} \\ q=100\%+8\%=1+\frac{8}{100}=1.08 \\ {S}_1=4\pi \cdot r^2=4\cdot 3.1416\cdot 1.8882^2\doteq 44.804{\text{m}}^2 \\ S=\lceil q\cdot S_1\rceil =\lceil 1.08\cdot 44.804\rceil =49{\text{m}}^2 \end{gathered}$$

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