Slant surface

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.

Final 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⋅ 52≐78.5398 cm2 S2​=π⋅ r⋅ s=3.1416⋅ 5⋅ 13≐204.2035 cm2  V=31​⋅ S1​⋅ v=31​⋅ 78.5398⋅ 12≐314.1593 cm3   Verifying Solution:  S=S1​+S2​=78.5398+204.2035≐282.7433 cm2 t=S/S1​=282.7433/78.5398=518​=3.6

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