Deviation - slope angle

Calculate the volume and surface of the rotating cone if its height is 10 cm and the side has a deviation of 30° from the base plane.

Correct answer:

V =  3141.5927 cm3
S =  2030.7574 cm2

Step-by-step explanation:

h=10 cm α=30°=30  tan α= h:r  r=tanαh​=tan30° h​=tan30° 10​=0.5773510​=17.32051 cm  S1​=π⋅ r2=3.1416⋅ 17.32052≐942.4778 cm2  V=31​⋅ S1​⋅ h=31​⋅ 942.4778⋅ 10=3141.5927 cm3
sin α = h:s  s=sinαh​=sin30° h​=sin30° 10​=0.510​=20 cm  S2​=π⋅ r⋅ s=3.1416⋅ 17.3205⋅ 20≐1088.2796 cm2  S=S1​+S2​=942.4778+1088.2796≐2030.7574 cm2   Verifying Solution:   s2​=h2+r2​=102+17.32052​=20 cm s2​=s

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