Spherical cap

What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.

Result

S =  326.73 m2

Solution:

h=2 m D=20 m=>ρ=D/2=10 m  r2=(rh)2+ρ2 2rh=h2+ρ2 r=h2+ρ22h=22+10222=26 m S=2πrh=2π262=326.73 m2h = 2 \ m \ \\ D = 20 \ m => \rho = D/2 = 10 \ m \ \\ \ \\ r^2 = (r-h)^2+\rho^2 \ \\ 2rh = h^2+\rho^2 \ \\ r = \dfrac{ h^2 + \rho^2 }{ 2h} = \dfrac{ 2^2 + 10^2 }{ 2 \cdot 2} = 26 \ m \ \\ S = 2\pi r h = 2\pi \cdot 26 \cdot 2 = 326.73 \ \text{m}^2



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