Vertex angle - cone

The rotating cone has a height of 72 cm and an angle at the top of 72°. Determine the volume of a sphere with the same radius as the cone.

Correct answer:

V =  2952658.1248 cm³

Step-by-step explanation:

$$\begin{gathered} h=72\text{cm} \\ \phi =72°\to \text{rad}=72°\cdot \frac{\pi }{180}=72°\cdot \frac{3.1415926}{180}=1.25664=2\pi /5 \\ \cos \phi /2=h:r \\ r=h/\cos (\phi /2)=72/\cos (1.2566/2)\doteq 88.9969\text{cm} \\ V=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 88.9969^3=2952658.1248{\text{cm}}^3\doteq 2.953\cdot 10^6{\text{cm}}^3 \end{gathered}$$

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