Spherical cap

Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.

Result

v =  1.384 cm
r =  2.684 cm

Solution:

D=4.6 cm r1=D/2=4.6/2=2310=2.3 cm S=20 cm2  S=2 πr1.v v=S2π⋅ r1=202⋅ 3.1416⋅ 2.3≐1.384≐1.384 cmD=4.6 \ \text{cm} \ \\ r_{ 1 }=D/2=4.6/2=\dfrac{ 23 }{ 10 }=2.3 \ \text{cm} \ \\ S=20 \ \text{cm}^2 \ \\ \ \\ S=2 \ \pi r_{ 1 } . v \ \\ v=\dfrac{ S }{ 2 \pi \cdot \ r_{ 1 } }=\dfrac{ 20 }{ 2 \cdot \ 3.1416 \cdot \ 2.3 } \doteq 1.384 \doteq 1.384 \ \text{cm}
r2=r12+v2 r=r12+v2=2.32+1.3842≐2.6843≐2.684 cmr^2=r_{ 1 }^2 + v^2 \ \\ r=\sqrt{ r_{ 1 }^2+v^2 }=\sqrt{ 2.3^2+1.384^2 } \doteq 2.6843 \doteq 2.684 \ \text{cm}

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