Axial section

Calculate the volume and surface of a cone whose axial section is an equilateral triangle with side length a = 18cm.

Correct answer:

V =  1322.2597 cm³
S =  763.407 cm²

Step-by-step explanation:

$$\begin{gathered} a=18\text{ cm } \\ r=a\mathrm{/}2=18\mathrm{/}2=9\text{ cm } \\ h=\sqrt{3}\mathrm{/}2\cdot a=\sqrt{3}\mathrm{/}2\cdot 18=9\sqrt{3}\text{ cm}\doteq 15.5885\text{ cm } \\ V={\displaystyle \frac{1}{3}}\cdot \pi \cdot r^2\cdot h={\displaystyle \frac{1}{3}}\cdot 3.1416\cdot 9^2\cdot 15.5885=1322.2597{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} s=a=18\text{ cm } \\ S=\pi \cdot r^2+\pi \cdot r\cdot s=3.1416\cdot 9^2+3.1416\cdot 9\cdot 18=763.407{\text{cm}}^2 \end{gathered}$$

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