Hard cone problem

The cone's surface is 200 cm², and its height is 7 centimeters. Calculate the volume of this cone.

Correct answer:

V =  168.4906 cm3

Step-by-step explanation:

S=200 cm2 h=7 cm  S = π⋅ r2 + π⋅ r⋅ s s2 = r2 + h2 s = r2+h2​  S = π⋅ r2 + π⋅ r⋅ r2+h2​  r=π​⋅ h2π+2⋅ S​S​=3.1416​⋅ 72⋅ 3.1416+2⋅ 200​200​≐4.7943 cm  V=31​⋅ π⋅ r2⋅ h=31​⋅ 3.1416⋅ 4.79432⋅ 7≐168.4906 cm3   Verifying Solution:  s=r2+h2​=4.79432+72​≐8.4844 cm  S2​=π⋅ r2+π⋅ r⋅ s=3.1416⋅ 4.79432+3.1416⋅ 4.7943⋅ 8.4844=200 cm2

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