Surface area

The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.

Correct result:

S =  711.64 cm2

Solution:

$S_1 = 100 \ cm^2 \ \\ V = 1000 \ cm^3 \ \\ S_1 = \dfrac{ 2r h }{2} \ \\ rh = 100 \ \\ h = 100/r \ \\ V = \dfrac13 \pi r^2 h \ \\ V = \dfrac13 \pi r^2 100 /r \ \\ V = \dfrac{ 100 }{3} \pi r \ \\ r = 9.55 \ cm \ \\ h = 100 / r = 10.47 \ cm \ \\ \ \\ s = \sqrt {r^2 + h^2 } = 14.17 \ cm \ \\ \ \\ S = \pi r (r+s) = \pi 9.55 \cdot (9.55+14.17) = 711.64 \ \text{cm}^2 \ \\$

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