Determine 81311

The surface of the rotating cone and its base area is in the ratio 18:5. Determine the volume of the cone if its body height is 12 cm.

Correct answer:

V =  314.1593 cm3

Step-by-step explanation:

v=12 cm S:S1 =18:5  S1 = π r2 S = π r2 + π r s  18/5 =   π r2 π r2 + π r s 18/5 =   r r + s 13r=5s  s2 = r2 + v2 s2 = (5/13s)2 + v2  s=v/1(5/13)2=12/1(5/13)2=13 cm  r=5/13 s=5/13 13=5 cm  S1=π r2=3.1416 5278.5398 cm2 S2=π r s=3.1416 5 13204.2035 cm2  V=31 S1 v=31 78.5398 12314.1593 cm3   Verifying Solution:  S=S1+S2=78.5398+204.2035282.7433 cm2 t=S/S1=282.7433/78.5398=518=3.6

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