Hectoliters - reservoir

The reservoir has the shape of a sphere with a diameter of 10 m. How many hectoliters of water is in it when it is filled to 90%? How many kg of paint are needed for painting if it is painted twice, and 1 kg of paint is enough for 6 square meters?

Correct answer:

x =  4712.389 hl
m =  104.7198 kg

Step-by-step explanation:

$$\begin{gathered} D=10\text{m} \\ r=D/2=10/2=5\text{m} \\ q=90\%=\frac{90}{100}=\frac{9}{10}=0.9 \\ V=q\cdot \frac{4}{3}\cdot \pi \cdot r^3=0.9\cdot \frac{4}{3}\cdot 3.1416\cdot 5^3\doteq 471.2389{\text{m}}^3 \\ x=V\to \text{hl}=V\cdot 10\text{hl}=471.2389\cdot 10\text{hl}=4712.389\text{hl}=4712.389\text{hl} \end{gathered}$$

$$\begin{gathered} n=2 \\ Q=6{\text{m}}^2\text{/kg} \\ S=4\pi \cdot r^2=4\cdot 3.1416\cdot 5^2\doteq 314.1593{\text{m}}^2 \\ m=n\cdot S/Q=2\cdot 314.1593/6=104.7198\text{kg} \end{gathered}$$

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