# Cone

The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?

Result

α =  0 °

#### Solution:

$V=9.42 \ \\ h=10 \ \\ V=Sh/3 \ \\ S=3 \cdot \ V/h=3 \cdot \ 9.42/10=\dfrac{ 1413 }{ 500 }=2.826 \ \\ S=\pi r^2 \ \\ r=\sqrt{ S/\pi }=\sqrt{ 2.826/3.1416 } \doteq 0.9484 \ \\ α=180/\pi \cdot \ \arctan(h/r)=180/3.1416 \cdot \ \arctan(10/0.9484) \doteq 84.582 \doteq 0 ^\circ \doteq 0^\circ$

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