Axial section

Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.

Result

V =  136.5 cm3

Solution:

S=πa2(a2+a)=34πa2=168 cm2 a=4S3π=8.44 cm h=a2a22=7.31 cm  V=13πr2h=136.5 cm3S = \pi \cdot \dfrac{a}{2}(\dfrac{a}{2}+a) = \dfrac{3}{4}\pi a^2 = 168 \ cm^2 \ \\ a = \sqrt{ \dfrac{4S}{3\pi}} = 8.44 \ cm \ \\ h = \sqrt {a^2-\dfrac{a^2}{2}} = 7.31 \ cm \ \\ \ \\ V = \dfrac{1}{3} \pi r^2 h = 136.5 \ \text{cm}^3



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