Cone A2V

The lateral surface of a cone, when unrolled flat, forms a circular sector with a central angle of 126° and an area of 415 cm².

Calculate the volume of the cone.

Final Answer:

V =  881.1 cm³

Step-by-step explanation:

$$\begin{gathered} \phi =126\cdot \frac{\pi }{180}=126\cdot \frac{3.1416}{180}\doteq 2.1991\text{rad} \\ S=415{\text{cm}}^2 \\ S=\pi s^2\cdot \phi /(2\pi ) \\ s=\sqrt{2\cdot S/\phi }=\sqrt{2\cdot 415/2.1991}\doteq 19.4274\text{cm} \\ r=\phi \cdot s/(2\pi )=2.1991\cdot 19.4274/(2\cdot 3.1416)\doteq 6.7996\text{cm} \\ h=\sqrt{s^2-r^2}=\sqrt{19.4274^2-6.7996^2}\doteq 18.1986\text{cm} \\ V=\frac{1}{3}\cdot \pi \cdot r^2\cdot h=\frac{1}{3}\cdot 3.1416\cdot 6.7996^2\cdot 18.1986=881.1{\text{cm}}^3 \end{gathered}$$

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