Rotary cone

The volume of the rotation of the cone is 967 cm3. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone.

Correct answer:

S =  444.02 cm2

Step-by-step explanation:

V=967 cm3 α=70   V = 31 π r2 h tan α =h:r = h/r  h = r tan α V = 31 π r3 tan α  r=3π tanα3 V=3π tan70° 3 V=33.1416 tan70° 3 967=33.1416 2.7474773 967=6.95272 cm  cos α = r:s = r/s s=cosαr=cos70° r=cos70° 6.9527=0.342026.9527=20.32839 cm S=π r s=3.1416 6.9527 20.3284444.0249 cm2   Verifying Solution:   h=s2r2=20.328426.9527219.1024 cm A=π180°arccos(r/s)=π180°arccos(6.9527/20.3284)=70 V2=31 π r2 h=31 3.1416 6.95272 19.1024=967 cm3



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