Cone - from volume surface area

The volume of the rotating cone is 1,018.87 dm3, its height is 120 cm. What is the surface area of the cone?

Correct result:

S =  679.1141 dm2

Solution:

V=1018.87 dm3 h=120 cm→ dm=120/10  dm=12 dm  V=13⋅ S1⋅ h  S1=3⋅ Vh=3⋅ 1018.8712=254.7175 dm2  S1=π⋅ r2 r=S1/π=254.7175/3.1416≐9.0044 dm   s2=h2+r2 s=h2+r2=122+9.00442≐15.0026 dm  S2=π⋅ r⋅ s=3.1416⋅ 9.0044⋅ 15.0026≐424.3966 dm2  S=S1+S2=254.7175+424.3966=679.1141 dm2

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