Axial cut

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

Correct answer:

V =  480.6611 cm³

Step-by-step explanation:

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

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