Rotary bodies

The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?

Correct result:

S1 =  199.5 cm2
S2 =  208.2 cm2

Solution:

V=180 cm3 h=15 cm  V=πr2 h/3 r1=3 V/π/h=3 180/3.1416/153.3851 cm s=h2+r12=152+3.3851215.3772 cm  S1=π r12+π r1 s=3.1416 3.38512+3.1416 3.3851 15.3772=199.5 cm2
V=πr2 h r2=V/π/h=180/3.1416/151.9544 cm  S2=2π r22+2π r2 h=2 3.1416 1.95442+2 3.1416 1.9544 15208.1988=208.2 cm2  S2>S1



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