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.

Result

S =  15.6 dm2

Solution:

h2=4r2r2 h=3r  V=13πr2h=13π3r3=7.1 l=7.1 dm3 r=37.1π3=1.58 dm  S=πrs=πr2r=2πr2 S=2π1.582=15.6 dm2h^2 = 4r^2-r^2 \ \\ h = \sqrt3 r \ \\ \ \\ V = \dfrac13 \pi r^2 h = \dfrac13 \pi \sqrt3 r^3 = 7.1 \ l = 7.1 \ dm^3 \ \\ r = \sqrt[3]{ \dfrac{ \sqrt3 \cdot 7.1 }{ \pi} } = 1.58 \ dm \ \\ \ \\ S = \pi r s = \pi r \cdot 2r = 2 \pi r^2 \ \\ S = 2 \pi 1.58^2 = 15.6 \ dm^2



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