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:

$v = 23 \ \\ S_1 = \pi r^2 \ \\ S_2 = \pi r s \ \\ \ \\ S_1 : S_2 = 7/9 \ \\ \dfrac{ \pi r^2} {\pi rs }= 7/9 \ \\ r / s = 7/9 \ \\ s = r \cdot 9 / 7; \ \\ \ \\ s^2 = v^2 + r^2 \ \\ r^2 \cdot 9^2/7^2 = 23^2 + r^2 \ \\ r^2 = \dfrac{ 529 }{ 1.653 - 1} \ \\ r^2 = 810.031 \ \\ r = \sqrt{ 810.031 } = 28.46 \ cm \ \\ \ \\ s = r \cdot 9 / 7 = 36.59 \ cm \ \\ \ \\ S_1 =\pi r^2 = \pi 28.46^2 = 2544.79 \ \text{cm}^2$
$S_2 =\pi rs = \pi \cdot 28.46 \cdot 36.59 = 3271.87 \ \text{cm}^2$

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