Two hemispheres

In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)?

Correct result:

S =  10.2102 cm2

Solution:

r=1 r2=r/2=1/2=12=0.5  S1=π r2=3.1416 123.1416 S2=π r22=3.1416 0.520.7854  S11=4π r2/2=4 3.1416 12/26.2832 S22=4π r22/2=4 3.1416 0.52/21.5708  S=S11+S22+S1S2=6.2832+1.5708+3.14160.785410.2102   Verifying Solution:  q=S/π/r2=10.2102/3.1416/12=134=3.25  S=134 π r2=10.2102 cm2



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