Sphere - parts

Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.

Result

S =  697.88 cm2

Solution:

r2=ρ2+(r−v)2 r2=ρ2+r2−2rv+v2 2rv=ρ2+v2 r=92+3.122⋅3.1=14.61 cm S=πrρ+2πrv=πr(ρ+2v)=697.88 cm2r^2=\rho^2+(r-v)^2 \ \\ r^2=\rho^2+r^2-2rv + v^2 \ \\ 2rv = \rho^2+ v^2 \ \\ r = \dfrac{ 9^2 + 3.1^2 }{ 2 \cdot 3.1 } = 14.61 \ cm \ \\ S=\pi r \rho+ 2\pi r v= \pi r(\rho+2v) = 697.88 \ \text{cm}^2

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