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 answer:

k1 =  1.5
k2 =  1.5

Step-by-step explanation:

D=h r = h/2 V1 = π r2 h = 2π r3  V2 = 34 π r3  k1 = V1/V2 =  34 π r32 π r3  k1=342=23=121=1.5
S1 = 2 π r2 + 2 π r h = 2 π r2 + 4 π r2 S1 = 6 π r2  S2 = 4 π r2  k2 = S1/S2 =  4 π r26 π r2  k2=46=23=121=1.5



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