Funnel

The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water.

Correct answer:

S =  15.6 dm²

Step-by-step explanation:

$$\begin{gathered} h^2=4r^2-r^2 \\ h=\sqrt{3}r \\ V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi \sqrt{3}{r}^3=7.1l=7.1d{m}^3 \\ r=\sqrt[3]{\frac{\sqrt{3}\cdot 7.1}{\pi }}=1.58dm \\ S=\pi rs=\pi r\cdot 2r=2\pi r^2 \\ S=2\pi 1.58^2=15.6{\text{dm}}^2 \end{gathered}$$

Try another example