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.

Correct 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 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 }=1.384 \ \text{cm}
r2=r12+v2 r=r12+v2=2.32+1.3842=2.684 cmr^2=r_{1}^2 + v^2 \ \\ r=\sqrt{ r_{1}^2+v^2 }=\sqrt{ 2.3^2+1.384^2 }=2.684 \ \text{cm}



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