Volume ratio

Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone.

Correct result:

r =  8:1

Solution:

a=1  r1=3/3⋅ a=3/3⋅ 1≐0.5774 r2=3/6⋅ a=3/6⋅ 1≐0.2887   V1=43⋅ π⋅ r13=43⋅ 3.1416⋅ 0.57743≐0.8061 V2=43⋅ π⋅ r23=43⋅ 3.1416⋅ 0.28873≐0.1008  r=V1V2=0.80610.1008≈8=8:1

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