Development angle of the cone

A numerical example sums up the calculation of the slant height, the volume, the lateral surface area and the development angle of a cone.

Example — Cone: calculating the development angle

Cone with radius $r=3$ and height $h=4$. Slant height: $\ell=\sqrt{9+16}=5.$ Development angle: $\beta = 360°\cdot \tfrac{3}{5} = 216°.$ Moreover $V = \tfrac{1}{3}\pi\cdot 9\cdot 4 = 12\pi, \qquad S_{\text{lat}} = \pi\cdot 3\cdot 5 = 15\pi.$

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Topics: Synthetic geometry of space
Concepts: Cone · Circular sector · Planar development
Skills: Calculating · Using formulas