Equilateral cylinder

A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.

Correct result:

k1 =  1.5
k2 =  1.5

Solution:

D=h r=h/2 V1=πr2 h=2πr3  V2=43πr3  k1=V1/V2=2 πr343πr3  k1=243=32=1 12=1.5
S1=2 πr2+2 πrh=2 πr2+4 πr2 S1=6 πr2  S2=4 πr2  k2=S1/S2=6 πr24 πr2  k2=64=32=1 12=1.5



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