Sphere slices

Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.

Correct result:

V =  18984.5 dm3
S =  3441.5 dm2

Solution:

 v2=r12r22+v22v=312922+252225=137.56cm r=r22+v22=922+137.562=165.49cm  V=43πr3=431000π165.493=18984.5 dm3 \ \\ v_2 = \dfrac{ | r_1^2-r_2^2+v^2 | }{2v} = \dfrac{ | 31^2-92^2+25^2 | }{2 \cdot 25} = 137.56 cm \ \\ r = \sqrt{ r_2^2 + v_2^2 } = \sqrt{ 92^2 + 137.56^2} = 165.49 cm \ \\ \ \\ V = \dfrac{4}{3} \pi r^3 = \dfrac{4}{3 \cdot 1000 } \pi \cdot 165.49^3 = 18984.5 \ \text{dm}^3
S=4πr2=4π165.492100=3441.5 dm2S = 4 \pi r^2 = \dfrac{ 4\pi \cdot 165.49^2}{100} = 3441.5 \ \text{dm}^2



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