# 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:

$A=126 \cdot \ \dfrac{ \pi }{ 180 }=126 \cdot \ \dfrac{ 3.1416 }{ 180 } \doteq 2.1991 \ \text{rad} \ \\ S=415 \ \text{cm}^2 \ \\ \ \\ S=\pi s^2 \cdot \ A / (2 \pi) \ \\ \ \\ s=\sqrt{ 2 \cdot \ S/A }=\sqrt{ 2 \cdot \ 415/2.1991 } \doteq 19.4274 \ \text{cm} \ \\ r=A \cdot \ s/(2 \pi)=2.1991 \cdot \ 19.4274/(2 \cdot \ 3.1416) \doteq 6.7996 \ \text{cm} \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 19.4274^2-6.7996^2 } \doteq 18.1986 \ \text{cm} \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r^2 \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 6.7996^2 \cdot \ 18.1986 \doteq 881.1169 \doteq 881.1 \ \text{cm}^3$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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