# Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2.

Calculate the volume of a cone.

Result

V =  881.1 cm3

#### Solution:

$A = 126 \cdot \ \dfrac{ \pi }{ 180 } = 126 \cdot \ \dfrac{ 3.1416 }{ 180 } \doteq 2.1991 \ rad \ \\ S = 415 \ cm^2 \ \\ \ \\ S = \pi s^2 \cdot \ A / (2 \pi) \ \\ \ \\ s = \sqrt{ 2 \cdot \ S/A } = \sqrt{ 2 \cdot \ 415/2.1991 } \doteq 19.4274 \ cm \ \\ r = A \cdot \ s/(2 \pi) = 2.1991 \cdot \ 19.4274/(2 \cdot \ 3.1416) \doteq 6.7996 \ cm \ \\ h = \sqrt{ s^2-r^2 } = \sqrt{ 19.4274^2-6.7996^2 } \doteq 18.1986 \ cm \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r^2 \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 6.7996^2 \cdot \ 18.1986 \doteq 881.1169 = 881.1 \ cm^3$

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