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?

Correct answer:

α =  0 °

Step-by-step explanation:

$$\begin{gathered} V=9.42 \\ h=10 \\ V=Sh\mathrm{/}3 \\ S=3\cdot V\mathrm{/}h=3\cdot 9.42\mathrm{/}10={\displaystyle \frac{1413}{500}}=2.826 \\ S=\pi r^2 \\ r=\sqrt{S\mathrm{/}\pi }=\sqrt{2.826\mathrm{/}3.1416}\doteq 0.9484 \\ \alpha =180\mathrm{/}\pi \cdot \arctan (h\mathrm{/}r)=180\mathrm{/}3.1416\cdot \arctan (10\mathrm{/}0.9484)\doteq 84.582=0^{\circ }=0^{\circ } \end{gathered}$$

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