Reservoir - water tank

The reservoir has the shape of a sphere with a diameter of 14 m.

a) How many hectoliters (hl) of water can it hold?
b) How many kg of paint is needed to paint the reservoir if it is painted three times and one kg of paint is enough to paint about 9 m²?

Final Answer:

V =  14367.55 hl
m =  205.25 kg

Step-by-step explanation:

$$\begin{gathered} D=14\text{m} \\ \sigma =9{\text{m}}^2\text{/kg} \\ n=3 \\ r=D/2=14/2=7\text{m} \\ {V}_1=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 7^3\doteq 1436.755{\text{m}}^3 \\ V=V_1\to \text{hl}=V_1\cdot 10\text{hl}=1436.755\cdot 10\text{hl}=14367.55\text{hl}=14367.55\text{hl} \end{gathered}$$

$$\begin{gathered} S=4\pi \cdot r^2=4\cdot 3.1416\cdot 7^2\doteq 615.7522{\text{m}}^2 \\ {m}_1=S/\sigma =615.7522/9\doteq 68.4169\text{kg} \\ m=n\cdot m_1=3\cdot 68.4169=205.25\text{kg} \end{gathered}$$

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