Two bodies

The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and second bodies.

Correct result:

r =  1:2

Solution:

a=8 cm b=4 cm  r1=b=4=4 cm h1=a=8=8 cm  S1=2π r12+2π r1 h1=2 3.1416 42+2 3.1416 4 8301.5929 cm2  r2=a=8=8 cm h2=b=4=4 cm  S2=2π r22+2π r2 h2=2 3.1416 82+2 3.1416 8 4603.1858 cm2  r=b:a r=S1/S2=301.5929/603.1858=12=0.5=1:2



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