# Axial cut

The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.

Result

V =  480.661 cm3

#### Solution:

$S=388.84 \ \text{cm}^2 \ \\ s=2r \ \\ S=\pi r^2 + \pi r s=\pi r (r+s) \ \\ S=\pi r (r + 2r )=3 \ \pi r^2 \ \\ \ \\ r=\sqrt{ S / (3 \pi) }=\sqrt{ 388.84 / (3 \cdot \ 3.1416) } \doteq 6.4232 \ \text{cm} \ \\ s=2 \cdot \ r=2 \cdot \ 6.4232 \doteq 12.8464 \ \text{cm} \ \\ \ \\ h^2=s^2 - r^2 \ \\ h=r \cdot \ \sqrt{ 3 }=6.4232 \cdot \ \sqrt{ 3 } \doteq 11.1253 \ \text{cm} \ \\ \ \\ V=\pi \cdot \ r^2 \cdot \ h/3=3.1416 \cdot \ 6.4232^2 \cdot \ 11.1253/3 \doteq 480.6611 \doteq 480.661 \ \text{cm}^3$

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