Calculate a cone

The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone.

Final Answer:

S =  65.3035 cm²
V =  33.9837 cm³

Step-by-step explanation:

$$\begin{gathered} h=5\text{cm} \\ \alpha =63{}^{\circ } \\ r=h/\tan \alpha =h/\tan 63°=5/\tan 63°=5/1.962611=2.54763\text{cm} \\ s=h/\sin \alpha =h/\sin 63°=5/\sin 63°=5/0.891007=5.61163\text{cm} \\ P=\pi \cdot r^2=3.1416\cdot 2.5476^2\doteq 20.3902{\text{cm}}^2 \\ S=P+\pi \cdot r\cdot s=20.3902+3.1416\cdot 2.5476\cdot 5.6116{\text{cm}}^2=65.3035{\text{cm}}^2 \end{gathered}$$

$V=\frac{1}{3}\cdot P\cdot h=\frac{1}{3}\cdot 20.3902\cdot 5=33.9837{\text{cm}}^3$

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