Cone and the ratio

Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.

Correct result:

S1 =  2544.79 cm2
S2 =  3271.87 cm2

Solution:

v=23 S1=πr2 S2=πrs  S1:S2=7/9 πr2πrs=7/9 r/s=7/9 s=r⋅9/7;  s2=v2+r2 r2⋅92/72=232+r2 r2=5291.653−1 r2=810.031 r=810.031=28.46 cm  s=r⋅9/7=36.59 cm  S1=πr2=π28.462=2544.79 cm2
S2=πrs=π⋅28.46⋅36.59=3271.87 cm2

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