Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.

Result

V =  106.57 cm3

Solution:

s=15 cm r=63360 s=63360 15=218=2.625 cm h2=s2r2 h=s2r2=1522.625214.7685 cm V=13 π r2 h=13 3.1416 2.6252 14.7685106.5674106.57 cm3s=15 \ \text{cm} \ \\ r=\dfrac{ 63 }{ 360 } \cdot \ s=\dfrac{ 63 }{ 360 } \cdot \ 15=\dfrac{ 21 }{ 8 }=2.625 \ \text{cm} \ \\ h^2=s^2 - r^2 \ \\ h=\sqrt{ s^2 - r^2 }=\sqrt{ 15^2 - 2.625^2 } \doteq 14.7685 \ \text{cm} \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r^2 \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 2.625^2 \cdot \ 14.7685 \doteq 106.5674 \doteq 106.57 \ \text{cm}^3



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