Funnel

The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 8.1 liters of water.

Final Answer:

S =  17.04 dm²

Step-by-step explanation:

$$\begin{gathered} V=8.1\text{l}\to {\text{dm}}^3=8.1\cdot 1{\text{dm}}^3=8.1{\text{dm}}^3 \\ {h}^2=4r^2-r^2 \\ h=\sqrt{3}r \\ V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi \sqrt{3}{r}^3 \\ r=\sqrt[ \\ 3]{\frac{\sqrt{3}\cdot V}{\pi }}=\sqrt[ \\ 3]{\frac{\sqrt{3}\cdot 8.1}{3.1416}}\doteq 1.6468\text{dm} \\ S=\pi rs=\pi r\cdot 2r=2\pi r^2 \\ S=2\pi \cdot r^2=2\cdot 3.1416\cdot 1.6468^2=17.04{\text{dm}}^2 \end{gathered}$$

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